How do I compute magnetic flux?

[austin007]

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)

 

[Fightfish]

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

 

[austin007]

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.

 

[Fightfish]

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)

 

[austin007]

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?

 

[Fightfish]

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 into obtain the solution at that point.

 

[rl.bhat]

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 )