PH 1120 Term B, 1996 Study Guide 4

PH1120 Term B,1997

STUDY GUIDE 4

Objective 13 The Biot-Savart Law

a) Calculate the contribution made to the magnetic field at a specified point by a current element, given the current, location, and orientation of the element.
b) Describe how the Biot-Savart law can be applied to calculate the net magnetic field produced at a point by a wire made of straight sections, and at the center of a current loop.
c) Calculate the magnetic force between two parallel conductors
d) Define the ampere Suggested Study Procedures Read Sec. 29-1 and 29-2. Study Sec. 29-3 and, in particular, Example 29-2 which is a direct application of the Biot-Savart Law. Study Sec. 29-4. While the mathematics is somewhat complicated, pay attention to the direction of the field at P (in Fig. 29-5) due to the current element, the fact that the distances of the current elements to P change as one moves along the wire, and that the field produced by a very long wire reduces to a simple expression. Study Example 29-3.

A direct application of the material in Sec. 29-4 is found in Sec. 29-5 in which the definition of the ampere is presented. Study Example 29-5. Study Sec. 29-6. Notice how the expression for the field at the center of the loop (Eq. 29-17 obtained by letting x be zero in Eq. 29-16) differs from that near a long wire.

Suggested Exercises and Problems Related to Objective 13

Exercises: 29-6, 29-12, 29-15, 29-19, 29-21

Problems: 29-43, 29-55, 29-56

Also this one:

A current element of length 0.003 m carrying a current of 6 A in the ( i + j) / Ö 2 direction is located at the origin.

Calculate the current element's contribution to the B-field at the following points:

a) (3,0,0) m d) (2,2,0) m

b) (0,2,0) m e) (-2,2,0) m

c) (0,0,2) m

Objective 14 Ampere's Law a) Describe the meaning of the line integral

(sometimes called the circulation of B) around a closed path.
b) Given two or more wires carrying specified current, determine the circulation of B on a given closed path.
c) Given a long straight wire carrying a given current, determine the magnetic field at a point a distance r from the wire.
d) Determine the magnetic field of a solenoid Suggested Study Procedures Study Secs. 29-7 and 29-8, and the Examples 29-8, 29-9, and 29-10. The three main situations where we will find Ampere's Law to be useful are the calculations of the fields near a long wire, near a cylindrical current distribution (like coaxial cable), and inside a solenoid. Suggested Exercises Related to Objective 14: Exercises: 29-22, 29-25, 29-28, 29-29 Objective 15 Magnetic Flux

a)Define magnetic flux

b)Define an area as a vector

c) Calculate the magnetic flux through an area positioned in a magnetic field

Suggested Study Procedure

Study Sec. 28-4 and Example 28-2. Study Sec. 23-3 earlier in the text to see how an area can be represented by a vector. Note also that although the definition of flux implies something passing through an area and having a direction, flux is defined explicitly as a scalar quantity. Study Example 23-1 imagining that the disk is in a uniform magnetic field.

Exercises and Problems Related to Objective 15

Exercises: 28-8 and 28-11

Problem: Do this one. A cube of edge length l = 0.15 m is positioned as shown. There is a uniform magnetic field

B = (5 i + 3 j + 1.5 k) T

through the region. Calculate the flux through each face of the cube. What is the total flux through all six faces of the cube?

Objective 16 Faraday's Law and Lenz's Law

Given a circuit in a magnetic field where

a) the B-field changes with time; or

b) the area of the circuit changes with time, or

c) the orientation of the circuit in the B-field changes with time;

determine:

i) the flux of the magnetic field intercepted by the circuit at a specified instant;

ii) the emf induced in the circuit;

iii) the current in the circuit (assuming the resistance is known).

For the situations above, using Lenz's Law determine the directions of theinduced currents.

Suggested Study Procedures

Study Secs. 30-1, 30-2 and 30-3. Examples 30-1 and 30-2 involve magnetic field changing in time. Example 30-4 involves an induced Emf resulting from a changing angle between the B field and the area vector. Study this example carefully paying particular attention to Figure 30-7. Example 30-7 involves an induced Emf resulting from a changing area. We revisit this later.

Lenz's Law, related to the conservation of energy, helps us to determine the direction of an induced current. Study Sec. 30-4 and pay particular attention to Example 30-10. Study Sec. 30-5 and Example 30-11. Read Sec. 30-6 to see how a changing magnetic flux can create an electric field which differs from an electrostatic field in that it is nonconservative.

Suggested Exercises and Problems Related to Objective 16

Exercises: 30-1, 30-3, 30-8. 30-10, 30-13, 30-15, 30-19, 30-20, 30-21
Problems: 30-34, 30-40, 30-41

HOMEWORK ASSIGNMENTS FOR STUDY GUIDE 4

Homework Assignment #13 - due in lecture Wednesday, Dec. 10
1) a) The current in a lightning bolt may be as much as 2 x 10 ⁴ A.

What is the magnitude of the magnetic field at a distance of 1.5 m from a lightning bolt? The bolt can be regarded as a straight line of current.

b) A superconducting ring of radus 3.0 cm carries a current of 20 A in a clockwise direction.

i) What is the magnitude of the magnetic field at the center of the ring?

ii) Using i, j, and k axes of your choice, express the field at the center in vector notation.

2) Problem 29-23 in Young except I₁ =2.0A, I₂ =3.0A and I₃ =5.0A.

Homework Assignment #14 - due in lecture Friday, Dec. 12

Problem 29-47 in the text, but the point P is .75 m from I₂ as shown

d) What is the magnitude and direction of the magnetic field at a point midway between the two currents?

Homework Assignment #15 - due in lecture Monday, Dec. 15

1) Problem 30-2 but the radius of the coil is .050 m.

2) Problem 30-4 but the coil is .050 m in radius Homework Assignment #16 - due in lecture Wednesday, Dec. 17

Problem 30-14 in Young
Problem 30-41 in Young but the area goes to zero in 0.17s and B is 1.60T.