A square loop of sides "a" lies in the yz plane with one corner at the origin. A varying magnetic field B = k_y. points in the positive x direction and passes through the loop k is a constant). The magnetic flux through the loop is A) ka². B) ka²/2. C) ka³/2. D) ka³/3. E) None of these is correct.

Question

Quizplus · Accepted Answer

The magnetic flux through a loop is given by the formula:

Φ = ∫B·dA

where B is the magnetic field, dA is an infinitesimal area element, and the integral is taken over the entire surface of the loop.

In this problem, the loop is a square lying in the yz plane, with one corner at the origin. The magnetic field is given by:

B = kS1U1B1yS1U1B0.

This field points in the positive x direction, so it is perpendicular to the loop. Therefore, the magnetic flux through the loop is simply:

Φ = B·A

where A is the area of the loop. The area of a square with sides of length a is:

A = a^2

Substituting the given expression for B, we have:

Φ = kS1U1B1yS1U1B0·a^2

The y component of the loop's position vector is always equal to zero, since the loop lies in the yz plane. Therefore, we can simplify the expression for the magnetic flux as follows:

Φ = kS1U1B0·a^2

which is the same as choice C: kaS1U1P13S1S1P0/2.

A Square Loop of Sides "A" Lies in the Yz