# How do I compute magnetic flux?

A circular loop (with a radius of 10 cm) rotattes in a constant magnetic fiels, which has a magnitude of 1 T. At an instant when the angle between the magnetic field and the normal axis (to the plane of the loop) is equal to 10 degrees and is increasing at a rate of 20 degrees/s, what is the magnitude of the induced emf in the loop?

How do I compute magnetic flux? ( I know that farady's law can be used to find emf)

## Answers and Replies

Firstly, what do you understand by "magnetic flux"?

Firstly, what do you understand by "magnetic flux"?

It is the product of magnetic field, B and perpendicular surface area to B, A.

I know B which is 1 T, how do I get A especially the angle.

Consider the projection of the surface area of the loop onto the plane perpendicular to the magnetic field (sort of like the 'shadow'). (You can consider the loop in 2D - a straight line to simplify the analysis)

Consider the projection of the surface area of the loop onto the plane perpendicular to the magnetic field (sort of like the 'shadow'). (You can consider the loop in 2D - a straight line to simplify the analysis)

So is A = pi * r * r cos(10 deg + 20 deg * t) correct?

So is A = pi * r * r cos(10 deg + 20 deg * t) correct?
That would be the correct A (perpendicular) for any time t if the rate of increase remains constant over time. However, it would not help you solve the problem. You should formulate it in a generic fashion: A = pi * r * r cos (theta), solve for dA/dt, before substituting the relevant values in to obtain the solution at that point.

rl.bhat
Homework Helper

So is A = pi * r * r cos(10 deg + 20 deg * t) correct?
At any instant the magnetic flux φ = B*A*cosθ.
So induced emf e = - dφ/dt = -(-B*A*sinθ*dθ/dt )