## E&M 1

• Electric Forces and Fields
Coulombs Law, Electric Field Lines, Electric Flux, Gauss' law, Insulators and Conductors
• Electric Potential
Potential Difference, Potential Energy, Capacitance
• Current and Circuits
Electric Current, Resistance, Ohm's law, Electrical Energy and Power, EMF, Kirchhoff's Rules, RC Circuits
• Magnetism
Magnetic Fields, Magnetic Force, Biot-Savart Law, Ampere's Law, Magnetism in Matter
• Inductance
Faraday's law, Motional EMF, Lenz's Law, Self-Inductance, RL Circuits

### Problem 1:

A spherical cloud of charge of radius R has uniform charge density ρ.  At a distance r from the center of the charge distribution, with r < R, the magnitude of the electric field is

(A)  ρr3/(3ε0R2)   (B)  ρr2/(3ε0R)    (C)  ρr/(3ε0)    (D)  ρR2/(3ε0r)    (E)  ρR3/(3ε0r2)

### Problem 2:

The diagram shows electric field lines and equipotential lines for two charged conductors X and Y.  The charge on X is positive.  Which of the following statements is not correct?

(A)  The charges on X and Y are of the same sign.
(B)  The charge on X is greater than that on Y.
(C)  The electric field lines and the equipotential lines intersect each other at an angle of 90 degrees.
(D)  A test charge placed at point P would be in equilibrium under the action of the electric forces.
(E)  The electric potential at point P is less than it is at point Q, which is symmetrically located on the other side of X.

### Problem 3:

A thin, insulating shell of radius R just touches a thin infinite insulating plane as shown.  Both the shell and the plane have a uniform  charge density of σ C/m2.  What is the magnitude of the electric field at point P, which is a distance R above the plane and a distance R from the outside of the sphere?

(A)  σ/(4ε0)   (B)  (2σ/(4ε0))½    (C)  2σ/(4ε0))    (D)  σ/ε0    (E)  5½σ/(4ε0)

### Problem 4:

Four equal-magnitude point charges, two positive and two negative, are arranged at the corners of a square as shown.  Let V and E be the potential and the electric field magnitude, respectively, at the center of the square, and let V0 and E0 be the same quantities at the same point if only the upper left positive charge were present.  Which of the following expresses the values of V and E?

(A)  V = V0, E = E0   (B)  V = 4V0, E = 0     (C)  V = 0, E = 4E0     (D)  V = 4V0, E = 4E0     (E)  V = 0, E = 0

### Problem 5:

The most general motion of a charged particle in a uniform magnetic field is
(A)  a parabola
(B)  a hyperbola
(C)  a helix
(D)  an ellipse
(E)  a cycloid

### Problem 6:

Two rods are joined en-to-end as shown.  Both have a cross-sectional area of 0.01 cm2.  Each is 1 m long.  One rod is copper with a resistivity of 1.7*10-6 ohm-cm, and the other is iron with a resistivity of 10-5 ohm-cm.  What voltage is required to produce a current of 1 A in the rods?

(A) 0.117 V   (B)  0.0145 V     (C)  V = 0.0117 V     (D)  V = 0.00145 V     (E)  1.7*10-6 V

### Problem 7:

A circular ring of radius 10 cm is made out of wire of radius 1 mm.  The ring carries a steady current.  The magnetic field due to that current is measured at the center of the ring, where the magnitude is found to be Bc and at the surface of the wire, where it is found to be Bs.  The ratio Bs/Bc is most nearly

(A) 300   (B)  30     (C)  V = 3     (D)  V = 1/3     (E)  1/30

### Problem 8:

If the currents in two parallel wires are in the same direction the force between them

(A)  Is zero.
(B)  is repulsive and in the plane containing the wires.
(C)  is attractive and in the plane containing the wires.
(D)  is perpendicular to the plane containing the wires.
(E)  depends on the sigh of the current carriers.

### Problem 9:

The plane of a square wire loop 0.2 meter on a side is perpendicular to a 0.008 T magnetic field.  If the magnetic field is reduced to zero in 0.04 s, the average voltage induced in the loop during this time interval is

(A) 0.008 V   (B)  0.04 V     (C)  V = 0.2 V     (D)  V = 3.2 V     (E)  32 V

### Problem 10:

In the circuit shown the point marked e1 is raised instantaneously at time t0 from zero to a fixed positive potential.  If e2 is connected to a high-impedance DC oscilloscope input, the graph of its voltage as a function of time will most resemble which of the following graphs?