Kenneth

The right loop in the diagrammed circuit is a square with the length of a side being l = 80cm. The value of R is 3.0Ω. The battery provides an emf of 18V, and the magnetic field (which only passes through the right loop and points into the page at all times) varies in magnitude as a function of time according to:

B(t) = B0 + beta(t)^2, B0 = 0.1 Tesla, beta = 0.30 Tesla/s^2

a.At t = 0 the voltmeter reads 6.0 volts. Find the power output of the lightbulb at this time.

b.The lightbulb is observed to gradually get dimmer until it goes dark, and then gradually grows brighter again. Find the moment in time t when the bulb is dark. [Hint: Does Kirchhoff ’s loop rule apply in its usual form to all of the loops?]

Two long straight wires carrying currents cross orthogonally at a point we will call the origin. One wire carries twice as much current as the other, and it flows in a direction we’ll call the +x direction, while the current in the other wire moves in a direction we’ll call the +y direction. A point charge lies at rest in this x–y plane at rest, so naturally it experiences no magnetic force due to the currents. The charge is then given a sudden push and is made to move. A friend claims that they saw the charge move in a straight line after being pushed. Do you believe your friend, and if so, describe what circumstances must have been present. If you don’t believe your friend, explain why what they claim is impossible.

Which of the magnetic fields described below cannot exist in our current prevailing theory of magnetism? [Note: β is a constant in answers (c) and (d).]

Please refer to the image shown to look at the possible answer choices.

A thick wire of radius R carries a current into the page (see diagram). The current density within the wire is uniform. The magnetic field at the surface of the wire is measured to be B0.

a.Determine the direction of the magnetic field, based on the view given in the diagram.

b.Use Ampére’s law to determine the functional dependence of the magnitude of the magnetic field inside and outside the wire, and plot, as accurately as you can, that dependence on the axes provided below. The one data point you have been given has already been plotted for you.

A magnetic field is described by the formula:

B = 0.20 (T/m^2) * ((xy I hat) - (0.5y^2 j hat))

This field is caused by a current that is flowing parallel to the z-axis. Find how much of this current is flowing through the rectangle whose corners are positioned at these points in the x, y plane:

(0cm,0cm), (0cm, 2cm), (3cm, 2cm), (3cm, 0cm)

Find the resistance R for which no current will flow through the central segment of the network shown below.

Use the circuit diagrammed to the right to answer the questions below.

a.Find what the ammeter reads immediately after switch S1 is closed (switch S2 remains open).

b.After a very long time, switch S1 is reopened, and switch S2 is closed. Find the reading by the ammeter 6.0 seconds after S2 is closed.

The network shown to the right consists of a infinitely-repeating pattern of resistors, all with a resistance of 1Ωconnected to a 12V battery with negligible internal resistance. Find the current measured by the ammeter. [Hint: How is the circuit to the right of points A and B different from the circuit connected to the battery?]

A fragment of a circuit is shown to the right. The middle branch of the circuit consists of an unknown number of resistors in series. All of the resistors in the circuit, including the unseen resistors in the central branch, are identical. The ammeter in the top branch reads 10A (to the right), while the ammeter in the bottom branch reads 6A (to the left). How many resistors are in the middle branch?

a) n = 3

b) n = 4

c) n = 5

d) n = 6

e) none of the above

The battery in the circuit shown to the right is real (not ideal), which means it has a non-negligible internal resistance. In the circuit as it is shown, the battery lights the bulb, and then the switch is closed. What effect does this have on the brightness of the bulb? Explain.

Consider a system of capacitors connected to a battery as shown in the diagram to the right.

a.Compute the total energy transferred from the battery.

b.Compute the energy stored in the 4.80 uF capacitor.

A parallel-plate capacitor with a vacuum between its plates is charged by connecting it to a 12V battery, and after it is fully charged, the battery is disconnected. Next an insulator with a thickness equal to half the width of the gap in the original capacitor is sandwiched between two thin conducting plates and is inserted between the plates of the original capacitor. Finally, a voltmeter is connected to the arrangement where the battery used to be, and it shows a reading of 8.4V.

a.Find the dielectric constant of the insulator.

b.Find the percentage of potential energy change that occurs when the dielectric enters the capacitor, and indicate whether the change is an increase or a decrease.

A spherically-symmetric collection of charge produces an electrostatic potential field that depends only upon the distance from the origin. Suppose such a collection of charge produces an electrostatic potential given by the function to the right.

a.Compute the electric field as a function of r in both regions: 0<=r<=a and r>a.

b.Compute the charge density as a function of r. Is all of the charge the same sign?

c.Find the total charge in the collection.

d.Compute the potential energy stored by assembling this charge.

V(r) = ((p0(r^2))/(6e0)) * (1- (2r/3a)) when 0<r<=a

V(r) = ((p0(a^2))/(18e0) when r > a

Note that p0 and a are constants

A voltage difference is placed across the two ends of a rod made of conducting material and a current is measured through it.

a) Describe three ways that another rod made out of the same material can be made to conduct less current when the same voltage is applied.

b) Which, if any, of the three alterations described in part (a) works by reducing the electric field strength in the conductor? Explain.

Imagine pulling apart two charged parallel plates of a capacitor until the separation is twice what it was initially. It should not be surprising that the energy stored in that capacitor will change due to this action. Compare this change in potential energy due to this action for these two cases:

•the charged capacitor is disconnected from the battery that charged it before the plates are pulled apart

•the charged capacitor remains connected to the battery that charged it while the plates are pulled apart

If these come out to be the same, explain why they must be so. If they come out different, explain the mechanism behind their difference.

A dipole is placed such that its center is a distance l from the surface of a long, flat conductor with thickness 2l. Which of the image charge diagrams below would be an appropriate one to use to find the electric force on the dipole due to the conductor? [Note: All of the dipoles below make the same angle with the vertical.]

Find the charge density functions for the following electric fields, where α and β are constants.

E(x,y,z) = (x^2)y i + 2y/(z^3) j + xsin(z) k

E(r, phi, z) = (alpha + beta/r) r hat

E(r, theta, phi) = alpha/(r^3) r hat

A long cylinder of positive charge of uniform density p is centered on the -axis. A hole centered at (a,0,0) is drilled through this cylinder parallel to the -axis. Find the magnitude and direction of the electric field at all points within the hole.

A sphere of electric charge has a radius of a. Inside this sphere of charge, the magnitude of the electric field (which points radially outward) is measured to vary with the distance from the center of the sphere according to: E(r) = Br^2(it doesn’t vary with respect to the polar or azimuthal angles). Find the volume charge density of the sphere at its outer surface: p(a).

A dipole is placed such that its center is a distance l from the surface of a long, flat conductor with thickness 2l. Which of the image charge diagrams below would be an appropriate one to use to find the electric force on the dipole due to the conductor? [Note: All of the dipoles below make the same angle with the vertical.]