A circular loop of wire has its radius reduced in half in time Δt.A uniform magnetic field is at an angle of 60° to the plane of the coil,and the magnetic field doubles its intensity in the same time interval Δt.During this interval,what happens to the flux through the coil?
A)It increases.
B)It decreases.
C)It remains the same.
D)More information is needed to make this conclusion.

Question

Quizplus · Accepted Answer

The flux through a coil is given by the formula Φ=BAcosθ, where B is the magnetic field, A is the area of the coil, and θ is the angle between the magnetic field and the plane of the coil. Here, we are given that the magnetic field doubles its intensity, which means B = 2B0, where B0 is the initial magnetic field intensity. We are also given that the radius of the coil is reduced in half, which means the area of the coil is reduced by a factor of 4. Therefore, the new area is A/4 where A is the initial area. Finally, the angle between the magnetic field and the plane of the coil is 60°. 
Putting the given values in the formula, we get:
Φ = (2B0)(A/4)(cos60°)
Φ = (B0A/2)
Since the radius of the coil is reduced in half, the area of the coil is reduced by a factor of 4, therefore the flux through the coil reduces by a factor of 2. 
So, the answer is B) It decreases.

A Circular Loop of Wire Has Its Radius Reduced in Half