Question

A physicist measures the magnetic field at the center of a loop of wire with N number of turns (not a solenoid) and current I flowing through it. They then triple the number of coils and half the radius of the coil while keeping the current the same. How does the magnetic field compare in the new situation, B2, compared to the first measurement, B1?
a. B2 = (3/2)B1
b. B2 = 6B1
c. B2 = (2/3)B1
d. B2 = (1/6)B1
d. None of the above

Answer 1

Answer: B

Explanation:

1) Apply Ampere's Law to the loop

$\int{B*} \, ds = u_0I$

$B(2\pi r)=u_0NI$

The loop has a circumference of 2pir.

The current enclosed is multiplied by N because there is N distinct loops.

$B_1= \frac{u_0NI}{2\pi r}$

$B_2=\frac{u_0(3N)I}{2\pi(0.5r) }$

$B_2=6 B_1$

Answer is B