Question

Figure is an edge-on view of a 14 cm diameter circular loop rotating in a uniform

3.8×10^-2 T magnetic field. I solved part a by using

 φ= B A cos θ = Bπr² cosθ = (3.8 x 10^-2) π (.07)²cos (0 degrees)= 5.8 x 10^-4 Wb and got correct answer, 

but having trouble finding the right answer for part B.  I used same equation for part B and used cos (30)= got wrong answer.  Is there another equation for finding the answer with the other angles?

Part A

What is the magnetic flux through the loop when is 0 degrees ?

Express your answer to two significant figures and include the appropriate units.
=5.8×10−4 Wb
Correct

Part B
What is the magnetic flux through the loop when is 30 degrees ?
Express your answer to two significant figures and include the appropriate units.
=

Part C
What is the magnetic flux through the loop when is 60 degrees ?
Express your answer to two significant figures and include the appropriate units.
=

Part D
What is the magnetic flux through the loop when is 90 degrees ?
Express your answer to two significant figures and include the appropriate units.

Answer 1

Concepts and reason

The required concepts to solve the problem are magnetic field and magnetic flux.

First, using the relation between the magnetic field, magnetic flux, and area, find the magnetic flux through the loop when the angle is.

Then, using the relation between the magnetic field, magnetic flux, and area, find the magnetic flux through the loop when the angle is.

Then, using the relation between the magnetic field, magnetic flux, and area, find the magnetic flux through the loop when the angle is.

Finally, using the relation between the magnetic field, magnetic flux, and area, find the magnetic flux through the loop when the angle is.

Fundamentals

The magnetic flux is defined as the surface integral of the magnetic field passing through the area. The relation between the magnetic field, magnetic flux, and area is

Here, is the magnetic field and is the area.

The expression for magnetic flux is

Here, is the angle between the area vector and the magnetic field lines.

(A)

The area of the circular loop is,

Substitutefor.

Here, is the diameter andis the radius.

The equation for magnetic flux is,

Replacefor.

Then, the magnetic flux is,

Substitutefor, for,and for.

(B)

The equation for magnetic flux is,

Substitutefor, for,andfor.

(C)

The equation for magnetic flux is

Substitutefor, for,andfor.

(D)

The equation for magnetic flux is

Substitutefor, for,andfor.

Ans: Part A

Thus, the magnetic flux through the loop when the angle isis.

Part B

Thus, the magnetic flux through the loop when the angle isis.

Part C

Thus, the magnetic flux through the loop when the angle isis.

Part D

Thus, the magnetic flux through the loop when the angle isis.