**Exercise 19.55**

Part A = repulsive

Part B = Since the currents flow in opposite directions, then due to the right hand rule, the magnetic field induced by one wire will be in an opposite direction to that of the other wire.

Part C = 10 μT

Part D = 50 μT/m

**Solutions Below:**

Part A

Currents in opposite directions creates a repulsive field, currents in the same direction create an attractive field.

repulsive

Part B

Since the currents flow in opposite directions, then due to the right hand rule, the magnetic field induced by one wire will be in an opposite direction to that of the other wire.

Part C

Express your answer using two significant figures.

The magnetic field induced by current flowing through a straight wire is:

B = ((μ_{0} * I) / (4 * π * R)) * (sin(φ_{1}) + sin(φ_{2}))

Your class may or may not use this general formula, but φ_{1} and φ_{2} are just the angles above and below a line perpendicular to the straight wire. Basically, the straight wire gets divided into an infinite number of segments and the magnetic field from each segment is added up (through calculus) to reach a total. The φ’s are just the angles between each segment and a line that runs perpendicular between the wire and the point where the magnetic field is being measured. Since the wires in this problem can be assumed to be infinitely long (the problem doesn’t say otherwise), the φ’s both become π / 2, and the formula becomes:

B = ((μ_{0} * I) / (4 * π * R)) * (sin(π / 2) + sin(π / 2))

So:

B = ((μ_{0} * I) / (2 * π * R))

Therefore:

B = (1.2566*10^-6 * 5) / (2 * 3.14159 * 0.1)

B = 10 μT

10 μT

Part D

Express your answer using two significant figures.

The force from one wire on the other is equal to:

F = ILB

And since B was found to be 10 μT in Part C:

F = ILB

F = 5 * L * 0.000010

For length, use 1 m since this is a unit length problem:

F = 5 * 1 * 0.000010

F = 50 μT/m

This is sort of misleading because the 50 μT/m is just from one wire – the actual repulsive force is double this since there are two wires, but mastering physics just wants the force from 1 wire (50 μT/m)

50 μT/m