Question

These questions refer to the expression for the magnetic field at the center of the square solenoid. Assume: for all coils, each side of the square a = 4.87 cm and the length of the solenoid L = 47.8 cm.
NOTE: Everything must be in MKS units!
NOTE: μ_o = 1.26x10^-6 in MKS units (determined in question 1).

a) In procedure 1, you will plot B_max vs. N, the number of turns of the coil. Suppose you set the current of I = 1.55 A, and vary the number of turns of the coil (with a and L the same for each coil). Find the slope of this straight line.
slope = T/turn

b) In procedure 2, you will plot B_max vs. I. Suppose you use a coil with 181 turns, and vary the current I. Find:
- n, the number of turns per length: n = turns/m
- the slope of this straight line: slope = T/A

Answer 1

a = 4.87 cm = 0.0487 m

r = a / 2 = 0.0487 / 2 = 0.02435 m

L = 47.8 cm = 0.478 m and i = 1.55 A

a)

slope of this straight line

B = ₀ N i / 2 r

B / N = ₀ i / 2 r

B / N = 1.26 X 10^-6 X 1.55 / 2 X 0.02435

B / N = 1.953 X 10^-6 / 0.0487

B / N = 40.10 X 10^-6 T/turns

B / N = 40.10 T/turns

b)

the number of turns per length: n = turns/m

n = 181 / 0.478

n = 378.66 turns/m

slope of this straight line slope = 40.10 X 10^-6 X 378.66 / 1.55

slope = 15184.266 X 10^-6 T/A

slope = 0.015184266 T/A