A single circular loop of wire with radius 0.025 m carries a current of 6.0 A. It is placed at the center of a solenoid that has length 0.60 m, radius 0.075 m, and 1200 turns.
-Determine the value of the current in the solenoid so that the magnetic field at the center of the loop is zero tesla.

Question

A single circular loop of wire with radius 0.025 m carries a current of 6.0 A. It is placed at the center of a solenoid that has length 0.60 m, radius 0.075 m, and 1200 turns. 
-Determine the value of the current in the solenoid so that the magnetic field at the center of the loop is zero tesla.

Quizplus · Accepted Answer

At the center of the loop, the magnetic field due to the solenoid is given by:

B = μ₀nI

where μ₀ is the permeability of free space, n is the number of turns per unit length (i.e., n = N/L, where N is the total number of turns and L is the length of the solenoid), and I is the current in the solenoid.

Using the given values, we have:

n = N/L = 1200/0.6 = 2000 turns/m
μ₀ = 4π×10⁻⁷ T·m/A
r = 0.025 m

At the center of the loop, the magnetic field due to the loop is given by:

B = μ₀I/2r

Setting these two expressions equal to each other and solving for I, we get:

μ₀nI = μ₀I/2r

I = 2nr

Substituting the given values, we get:

I = 2 × 2000 turns/m × 0.075 m = 300 A

Therefore, the current in the solenoid that will produce a zero net magnetic field at the center of the loop is I = 300 A, which corresponds to choice C.

A Single Circular Loop of Wire with Radius 0