An infinitely long single wire with current I1 = 2.5 A and a rectangle wire loop with current I2 = 0.25 A are in the same plane as shown. The dimensions of the loop are a = 0.025 m and b = 0.025 m. The infinite wire is parallel to side AD of the loop and at a distance d = 0.025 m from it.

Randomized Variables

I1 = 2.5 A

I2 = 0.25 A

a = 0.025 m

b = 0.025 m

d = 0.025 m

Part (a) Express the magnitude of the magnetic force Fad, from I1 on wire AD in terms of I1, I2, d and the loop dimensions.

Part (b) Calculate the numerical value of Fad in N.

Part (c) Express the magnitude of the magnetic force Fbc, from I1 on wire BC in terms of I1, I2, a, b, and d.

Part (d) Calculate the numerical value of Fbc in N.

Part (e) Is the force of Fad repulsive or attractive?

Part (f) Is the force of Fbc repulsive or attractive?

Part (g) The forces of Fad and Fbc both act on the infinite wire I1. Do they sum to produce a net attractive or repulsive force?

Part (h) Calculate the numerical value of the sum of the forces F = Fab - Fbc on the infinite wire in N.

2nd question:

A solenoid is created by wrapping a L = 90 m long wire around a hollow tube of diameter D = 4.5 cm. The wire diameter is d = 0.9 mm. The solenoid wire is then connected to a power supply so that a current of I = 9 A flows through the wire.

Randomized Variables

L = 90 m

D = 4.5 cm

d = 0.9 mm

I = 9 A

Part (a) Write an expression for the number of turns, N, in the solenoid. You do not need to take into accountthe diameter of the wire in this calculation.

Part (b) Calculate the number of turns, N, in the solenoid.

Part (c) Write an expression for the length of the solenoid (L2) in terms of the diameter of the hollow tube D, assuming it is constructed by using only 1 layer of loops (note that most solenoids are actually constructed with many layers, to maximize the magnetic field density).

Part (d) Calculate the length of the solenoid (L2) in meters.

Part (e) Calculate the magnitude of the magnetic field at the center of the solenoid in Teslas.