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The equivalent resistance between points 1 and 2 of the circuit shown is
Positive and negative charges of the same magnitude, as well as a small positive test charge are placed as shown in each of the four figures.
Rank the magnitude of the force the test charge feels in each of the four figures.
A uniform magnetic field is directed into the page. A charged particle, moving in the plane of the page, follows a clockwise spiral of decreasing radius. A reasonable explanation is that
A stationary positive charge +Q is located in a magnetic field B, which is directed toward the right as indicated. The direction of the magnetic force on Q is
If you plug an electric hair dryer into a wall outlet and turn it on, current will flow through the wires inside the wall. Some power will be dissipated as heat in those wires. If you plug a second, identical hairdryer into the same outlet and turn it on, the amount of power wasted in the wires inside the wall will
The magnetic domains in a non-magnetized piece of iron are characterized by which orientation?
In the early universe and in stars, deuterium nuclei are produced from the combination of one proton and one neutron, with the release of a gamma ray. What is the charge on a deuterium nucleus in units of qe = 1.6*10-19 C?
A current loop lies in the xy-plane. It has a magnetic dipole moment of 0.1 A-m2 along the z-axis. A uniform 2 T magnetic field parallel to the xz-plane makes a 30° angle with the x-axis. What is the magnitude of the net torque on the current loop?
A bird sits on a high-voltage line. Why does the bird not get hurt?
The whole bird is at approximately the same potential, so there is no electric field across it.
The SI unit of capacitance is Farad (F). This is the same as
The inner and outer surfaces of a cell membrane carry a negative and positive charge respectively. Because of these charges, a potential difference of about 70 mV exists across the membrane. The thickness of the membrane is 8 nm. If the membrane were empty (filled with air), what would the magnitude of the electric field inside the membrane be in units of 106 N/C = 106 V/m?
If the dielectric constant of the membrane in the previous problem, with the same membrane potential V = 70 mV, is κ = 9, what would the magnitude of the electric field be inside the membrane?
A 9 V battery is rated at 80 Ah. It can deliver a current of 80 A for one hour, or a current of 40 A for 2 hours, etc. What is the total energy stored in the battery?
Three resistors connected in series carry currents I1, I2 and I3, respectively. Which of the following expresses the value of the total current IT in the system made up of the three resistors?
IT = I1 = I2 = I3
In the figure, field lines are drawn following the convention that 1 field line emerges from a small sphere with 1 pC of charge. An irregular closed surface is shown, the interior of which is hidden. The net amount of charge inside the closed surface must be
Consider the situation shown below. A wire carrying a current flowing into the page is placed between the poles of a horseshoe magnet. Which statement is correct regarding the magnetic force on the wire?
The magnetic force on the wire points towards the left.
Three charges are lined up in a row as shown. All the charges have the same magnitude.
If we compare the force charge q1 exerts on charge q3 ( F1→3) to the force q2 exerts on charge q3 ( F2→3), which statement is correct?
F1→3 is less than half as big as F2→3 .
What do you know already about atoms, elementary particles, and charges? Select multiple answers!
Protons and electrons have charges qe and –qe, respectively, where qe is the smallest quantum of charge.
Electrically neutral materials contain the same number of protons and electrons.
Neutral objects become negatively charged by acquiring additional electrons from other objects.
What do you already know about the electrostatic force that can exist between two interacting objects? Pick the correct statements from the choices below.
It depends on the net charge of each of the interacting objects.
It can be repulsive.
It can be attractive.
Two small objects each with a net charge of Q exert a force of magnitude F on each other. We replace one of these with a charge 4Q. What is the magnitude of the force after the
Four arrangements of charge are shown. Each charge has the same magnitude, but some are positive (+) and some are negative (-).
All distances are to the same scale. In which arrangement would the magnitude of the force felt by a positive test charge placed at P
be the largest?
Choose the force vector that correctly shows the direction o f t h e net force on charge B due to the other two charges. Charge is given in arbitrary units.
Clothes taken from a clothes dryer sometimes cling together. Consider a load of wool socks and cotton-polyester shirts.
The socks will cling to the shirts, but not to each other.
Instead of hitting the green puck, you move it using charges. All charges are negative. Which of the charge distributions below exerts the force with the smallest magnitude (near zero) on the puck?
All charges are positive. Which arrow best represents the direction of acceleration of the green puck as it passes just below the wall ?
All charges repel each other. When the puck passes the wall, the horizontal components of the forces due to the nearby charges cancel, the vertical components add.
The force due to the distant charge has a very small magnitude and does not contribute much to the sum.
What is the force (magnitude and direction) on a -5 μC charge located at x = 5 m from a -1 μC charge at the origin?
0.0018 N into positive x-direction
Two 10 μC charges are located at (x, y) = (0, 3m) and (3 m, 0), respectively. What is the magnitude of the force on the 1 μC charge at the origin?
Two negative point charges with the same charge -q and a point P are located as shown, at the vertices of an equilateral triangle. What is the direction of the electric field due to the two point charges at point P?
The –x direction
What is the direction of the electric field produced by the -5 μC charge located at x = 5 m at the position of the -1 μC charge at the origin?
When a positive charge is released from rest in a uniform electric field, it will
The red charge on the left is a positive 1 microCoulomb charge.
What is the magnitude and sign of the blue charge on the right?
The figure shows electric field lines representing the field due to three charges. Where does the electric field have the greatest magnitude?
Are all the diagrams below valid field line diagrams?
Compare the electric flux through surfaces (a) and (b). All charges have magnitude q.
The flux through both surfaces is q/ε0.
The flux through both surfaces is 0.
The flux through the right surface surfaces is 2q/ε0 while the flux through the left surface is q/ε0 .
None of the above.
What do you think will happen when a negatively charged balloon is moved towards the neutral wall?
What is the electrostatic potential energy of a -5μC charge located at x = 5 m and a -1 μC charge located at the origin?
Consider a uniform electric field, for example the field inside a parallel plate capacitor, as shown. If an electron is taken from location B to location C, how does its potential energy change?
The charges in the groups A and B below are all given in units of Q. Which group of charges took less work to bring together from infinity?
Which requires zero work, to move a positive point charge from point P to point 1, 2, 3, or 4? All those points are the same distance from P.
Which requires the most positive work done by an external force, to move a positive point charge from point P to point 1, 2, 3, or 4? All those points are the same distance from P.
Location P is equidistant from the two charges of an electric dipole. The voltage at P is
Two 10 μC charges are located at (x, y) = (0, 3m) and (3 m, 0), respectively. What is the potential due to those two charges at the location of the 1 μC charge at the origin?
Assume that the potential difference between the positive and negative plate is 100 V. A proton travels from the positive to the negative plate.
Its kinetic energy increases by 1.6*10-17 J = 100 eV.
1 eV= 1.6 *10^-19 J
The graph below shows a contour map of the equipotential surfaces due to 3
point charges. point P.
~800 V/m down
A diagram of an irregularly shaped charged conductor is shown below. Four locations along the surface are labeled A, B, C, and D. Rank these locations in increasing order of the strength of the electric field just outside the surface, beginning with the smallest electric field
A parallel-plate capacitor initially is connected to a battery and the plates hold charge ±Q. The battery is then disconnected. If the plate spacing is now doubled, what happens?
Which diagram does not represent an electrical current?
In a storm, falling raindrops carry a current density of +1.0*10-6 A/m2 towards the ground. If 100 drops strike each square meter of ground per second, calculate the magnitude and sign of the average charge on each raindrop in Coulomb.
+1.0*10-6 A/m2 = +1.0*10-6 C/(s m2)
1.0*10-6 C/(s m2) = 100 drops/(s m2) * ? C/drop
A steady current moves through a circuit from the positive terminal of a battery to the negative terminal. What happens?
(a) The amount of current decreases with distance from the positive terminal.
(b) The voltage decreases with distance from the positive terminal. (c) Potential energy is converted into thermal energy.
To what extent is the flow of water analogous to the flow of charge?
What is NOT a correct hydrodynamic analog?
resistance – viscosity times function of geometry
charge – volume flow rate
pressure difference – voltage
Pump – battery
Capacitor – water storage tank
Two cylindrical copper wires have the same mass. Wire A is twice as long as wire B. How are their resistances are related?
Hint: same masssame volume
volume of a cylinder = area*length
What happens to the area when the length is doubled?
If electrical energy costs $0.10 for each kWh, what would it cost to raise a house of mass 5*105 kg (500 metric tons) a height of 1 m above the ground, using an electric motor of 50% efficiency?
Use g = 10 m/s2.
1 kWh = (1000 J/s)*3600 s = 3.6*106 J
mgh = (5*105 kg)*(10 m/s2)*(1m) = 5*106 J (5*106 J)*(1 kWh/ 3.6*106 J) = 1.39 kWh
50% efficiency 2.78 kWh are needed 2.78 kWh* $0.10/kWh = $0.28
If a resistor of resistance R is connected to a battery of voltage V, the equation for the power dissipated in the resistor, P = I2R, implies that a larger resistance R will dissipate more energy and get hotter than a smaller resistance.
What is the equivalent resistance between the points A and B?
A real, not ideal, battery is connected as shown. Rank the potential difference across the terminals from the greatest to the
Rank in order, from brightest to dimmest, the identical bulbs A to D.
A capacitor of 100 microFarads and a resistor of 1000 Ohms are in series. The circuit has a time constant of 0.1 s. What does this mean?
It takes several times 0.1 second to charge or discharge the capacitor.
The region of space around a moving proton contains
both an electric and a magnetic field.
Two parallel long wires each have a large current I flowing out of the page, as shown. In what direction does the magnetic field point at position P?
The magnetic field inside a solenoid (far from the edges) is measured to be 0.10 T. If the solenoid is 1.00 m long and carries a current of 6.625 A, how many turns does it have?
How should the field lines inside this bar magnet be drawn?
Approximately parallel from the South pole to the North pole.
An electron moves perpendicular to a magnetic field. A magnetic force acts on it in the direction shown. What is the direction of B?
Two parallel wires are carrying currents in opposite directions as shown. Wire #1 has a current I1 that is out of the page, whereas wire #2 has a current I2 that is into the page.
What effect does the magnetic field from wire #2 have on wire #1?
The field exerts a force on wire #1 (directed left).
An electron travels in a circular path perpendicular to a uniform magnetic field as shown. A proton also travels with the same speed in a circular path perpendicular to the same magnetic field.
Which particle follows the smaller circle?
The track ABC in the figure is a reproduction of the path of a charged particle in a cloud chamber. If the magnetic field is perpendicular to this sheet of paper and directed into the paper, the particle
has a negative charge and has moved from C to A.
Make a prediction! When we connect the power supply, the magnet will
turn (north pole towards coil) and be attracted.
A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic field, the net magnetic force on the loop is
Which statement is false?
There is no net force acting
on either loop.
There is no torque acting on loop A but a torque is acting on loop B.
Loop A has lower potential energy than loop B.
Loop A is in stable equilibrium and loop B is in unstable equilibrium.
A proton is initially at rest at x = d and an electron is initially at rest at x = -d. At the same instant they are released. They subsequently
fly away from each other.
collide close to x = -d.
collide at x = 0.
orbit each other.
collide close to x = d.
The electric field in the previous problem points
A uniform electric field with field strength E = 10 N/C pointing in the x-direction intersects a 2 m2 area in the y-z plane. What is the electric flux through this area?
Two balls rest on a frictionless surface. One ball is given a charge of +Q. The other ball is given a charge of +3Q. Which diagram best represents the magnitude and direction of the force vectors on the balls?
A cubical closed surface has N inward electric flux lines passing through one face and N outward electric flux lines passing through the opposite face as shown in the figure.
The flux lines exhibit convergence and there are no flux lines passing through any other face. If the magnitude of the electric field at the centre of the cube is E, the total charge inside the cube is
A point positive charge Q is placed at the centre of a cubical closed surface.
The outward electric flux through one pair of opposite faces of the cube is
What are the signs of the charges at points A and B?
A memory cell in a computer contains a capacitor to store charge. Charge being stored or not being stored corresponds to the binary digits 1 and 0. To pack the cells more densely, trench capacitors are often used in which the plates of a capacitor are mounted vertically along the walls of a trench etched into a silicon chip. If we have a capacitance of 50*10-15 F and each plate has an area of 30*10-12 m2 (micron-sized trenches), what is the plate separation?
The immediate cause of many deaths is ventricular fibrillation, an uncoordinated quivering of the heart as opposed to proper beating. An electric current discharged to the chest can cause momentary paralysis of the heart muscle, after which the heart will sometimes start organized beating again. A defibrillator is a device that applies a strong electric shock to the chest over a time interval of a few milliseconds. Assume that an energy of 300 J is to be delivered from the defibrillator, having a 30.0 microFarad capacitance. To what potential difference must the defibrillator be charged?
Which of the charge configurations depicted would give rise to the potential shown below?
Imagine assembling four equal charges, one at a time, and putting them at the corners of a square. Find the total work done by an external force to assemble these if the charges are each 5 microCoulomb and the square has 25 cm sides.
A solid, conducting sphere of radius R is positively charged. Of the following distances from the center of the sphere, which location will have the greatest electric potential? (Take V = 0 at r = infinity.)
In a series RC circuit a charged capacitor with capacitance C is being discharged though a resistor of resistance R. Plots of voltage and current versus time are shown below. Find the time constant τ of the circuit.
What is the resistance of the series RC circuit referred to in the previous problem?
What is the capacitance of the series RC circuit referred to in the previous problem?
When a light bulb is turned on, its resistance increases until it reaches operating temperature. What happens to the current in the bulb as it is warming up?
It decreases as the bulb warms up until the bulb reaches operating temperature.
What is the equivalent resistance of the circuit shown in the figure to the below? Each resistor is 1 Ω.
A bulb (i.e., a resistor) is connected in series to a switch, a battery, and an uncharged capacitor. At t = 0, the switch is closed. Which of the following best describes the brightness of the bulb as a function of time?
Analyze the circuit shown below to find the total power supplied by the battery in mW.
A wire along the y-axis carries a current of 10.0 A in the -y direction. There is a magnetic field 10-4 T in the +z direction. The magnetic force on a 1.0 m segment of this wire is
A proton is released near the equator and falls toward the earth under the influence of gravity. The magnetic force on the proton will be toward the
In the figure below, the cube is 40 cm on each edge. Four straight-line segments, ab, bc, cd, and da form a closed loop that carries a current I = 5 A. A uniform magnetic field B = 0.02 T is in the positive y-direction. What is the magnitude of the magnetic force on the wire segment da?
What is the direction of the magnetic force on the wire segment cd?
Point P is at a perpendicular distance x from each wire carry current I in the directions indicated. What is the magnetic field B at point P?
A mass spectrometer is to be used to separate protons from deuterium nuclei. A deuterium nucleus has the same charge and twice the mass as a proton, since it contains an extra neutron. Both the deuterium and the proton nuclei are accelerated by the same voltage. Which of the following statements is true?
The deuterium will have a larger radius of curvature, since it is more massive.
The paths of several particle moving through a region with a magnetic field pointing into the page are shown. Which particles are positively charged?
You have just pulled your clothes from the dryer and find that a sock is clinging to your jeans with static electricity. You pull the two apart. As the jeans and the sock move apart, the force between them becomes weaker because the
the force between the electric charges becomes weaker with increasing distance.
If the charge on each of two identical tiny spheres is doubled, while their separation is also doubled, their force of interaction
will stay the same.
A positive charge is placed at one of 3 locations in a region where the electric field is uniform. Compare the magnitude F of the electric force on the charge at the different locations.
F is the same at all locations, but not zero.
Which of the following statements is true?
A positive charge experiences an attractive electrostatic force toward a nearby neutral conductor.
A positive charge experiences no electrostatic force near a neutral conductor.
A positive charge experiences a repulsive force, away from a nearby conductor.
Whatever the force on a positive charge near a neutral conductor, the force on a negative charge is then oppositely directed.
A positive charge experiences an attractive electrostatic force toward a nearby neutral conductor.
Through rubbing an object has acquired a charge of -1 nanoCoulomb.
Electrons have been transferred to the object.
Three pithballs are suspended from thin threads. Various objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the pithballs is charged by touching them with one of these objects. In one set of experiments, it is found that pithballs 1 and 2 repel each other and that pithballs 2 and 3 attract each other. From this we can conclude that
The figure below shows the electric field lines for a system of two point charges. Point charge q1 has a charge of 6 microCoulomb. What is the charge of point charge q2?
Consider the 5 arrangements of charges below. (Electric Field Hockey Simulation) Which of the following statements is true?
1) All of the pucks feel a force to the right.
2) The puck in C feels a greater force to the right than the puck in D.
3) The puck in E feels a force to the right that is four times greater than that felt by the puck in B.
4) The net force on the puck in A is zero.
5) The puck in E feels a force to the right that is four times greater than that felt by the puck in D.
When an electromagnet has an iron core inserted, what happens to the strength of the magnet?
The voltage at the terminals of an automobile battery is 12.0 V when no current is drawn. When the starter motor is running, it draws a current of 100 A and the battery voltage falls to 10.0 V. What is the internal resistance of the battery?
Three pairs of conducting plates (capacitors) are shown in the figure below. Pair B has the same separation as pair A but twice the plate area. Pair C has the same area as pair A but half the separation between the plates. If each pair is connected to an identical battery so that the potential difference between each pair of plates is equal to the same value, ΔV, rank the pairs of plates by the magnitude of the electric field between the plates.
Two current loops have the same area and carry the same current I. Each is placed in a uniform magnetic field B, so that their magnetic moments μ point in opposite direction. (There is no interaction between the loops.) The magnetic moment of loop 1 is parallel to B and the magnetic moment of loop 2 is anti-parallel to B. The following statements are made.
(a) There is no torque acting on either loop.
(b) There is no net force acting on either loop.
(c) Loop 1 is in stable equilibrium and loop 2 is in unstable equilibrium.
(d) Both loops have the same potential energy.
Let E = 4 N/C in the x direction and B = 4 T in the -z direction. An electron is moving in the y-direction with speed 1m/s. What is the magnitude of the acceleration of the electron in m/s2?
Consider a very long solenoid with radius R and length L (R << L). The magnetic field at the center of the solenoid is B0. A second solenoid is constructed that has twice the radius, twice the length, and carries twice the current as the original solenoid, but has the same number of turns per meter. The magnetic field at the center of the second solenoid is
What is the time constant for the discharge of this capacitor?
Two +1 microCoulomb point charges are located on the x-axis, at x = 2 m and at x = -2 m. Find the magnitude of the electric field at the origin.
A particle with a positive charge moves in the xz-plane as shown. The magnetic field is in the positive z-direction. The magnetic force on the particle is in
the negative y-direction.
A charged insulator and an uncharged metal
The electric field-line diagram visualizes the electric field produced by a pair of charges. A negative test charge is placed at point P directly between the two charges in the diagram.
Equipotential lines are shown in the figure. What is the approximate magnitude of the electric field at point A?
Regarding the Earth and a cloud layer 800 m above the Earth as the plates of a capacitor, calculate the capacitance if the cloud layer has an area of (1 km)2. If an electric field of 3*106 N/C makes the air break down and conduct electricity, (that is, cause lightning,) what is the maximum charge (in C) the cloud can hold?
Assume that the potential V is higher at point A than at point B. Which statement then is correct?
A positive charge gains electrostatic potential energy when it moves from point B to point A.
A capacitor with a charge of 5 C has its terminals shorted by a metal wire so that the charge flows off within 2 s. What is the average current flowing during that time in Ampere (A)?
Determine the equivalent resistance between points A and B in the following circuit.
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