# Homework Assignment

Questions 1, 2, 3, 4, 9, 18, 19

Problems 30.8A, 22, 23, 25, 32, 40, 60, 64

Q1 Is the magnetic field created by a current loop uniform?

Q2 A current in a conductor produces a magnetic field that can be calculated using the Biot-Savart law. Since current is defined as the rate of flow of charge, what can you conclude about the magentic field produced by a stationary charge? What about moving charges?

Q3 Two parallel wires carry currents in opposite directions. Describe the nature of the resultant magnetic field created by the tewires at poinsts

(a) between the wires and

(b) outside th wires in a plane containing them.

Q4 Explain why two parallel wires carrying currents in opposite directions repel each other.

Q9 Describe the similarities between Ampere's law in magnetism and Gauss's law in electrostatics.

Q18 Will a nail be attracted to either pole of a magnet? Explain what is happening inside the nail when placed near a magnet.

Q19 The north-seeking ppole of a magnet is attracted toward the geographic North Pole of Earth. Yet, like poles reple. What is going on here?

30.8A, A conductor consists of a circular loop of radius R and two straight, long sections, as in Figure P30.8. The wire lies in the plane of the paper and carries a current I. Determine the magnitude and direction of the magnetic field at the center of the loop.

30.22, A closely wound, long solenoid of overall length 30.0 cm (0.30 m) has a magnetic field of 4.00 x 10 - 4 T at its center produced by a current of 1.00 A through its windings. How many turns of wire are on the solenoid?

30.23, A superconducting solenoid is to generate a magnetic field of 10.0 T.

(a) If the solenoid windings has 2000 turns/m, what is the required current?

(b) What force per unit length is exerted on the windings by this magnetic field?

30.25, Some superconducting alloys at very low temperatres can carry very high currents. For example Nb3Sn wire at 10 K can carry 1000 A and maintain its superconductivity. Determine the maximum value of B achievable in a solenoid of length 25 cm (0.25 m) if 1000 turns of Nb3Sn wire are wrapped on the outside surface.

30.32, In Figure P30.32, both currents are in the negative x direction.

(a) Sketch the magnetic field pattern in the yz-plane.

(b) At what distance d along the z-axis is the magnetic field a maximum?

30.40, Consider the hemispherical closed surface in Figure P30.40. If the hemisphere is in a uniform magnetic field that makes and angle theta with the vertical, calculate the magnetic flux through

(a) the flat surface S1 and

(b) the hemispherical surface S2.

30.60, A lightning bolt may carry a current of 10,000 A for a short period of time. What is the resulting magnetic field 100 m from the botl?

30.64 Two parallel conductors carry current in opposite directions as showin in Figure P30.64. One conductor carries a current of 10A. Point A is at the midpoint between the wires and point C is a distance d/2 to the right of the 10 A current. If d = 18 cm = 0.18 m and I is adusted so that the magnetic field at C is zero, find

(a) the value of the current I and

(b) the value of the magnetic field at A.