Question

A circular loop of wire with radius 0.100 m and resistance R = 5.00 Ω. The loop is placed in a magnetic field of strength B = 0.125 T, which can be rotated. The angle of the magnetic field with respect to the normal of the loop is θ(t), where t denotes the time. Initially, θ(0) = 2/π rad . The angular speed at which the magnetic field rotates is w= 60.0rads−1.
(a) Find an expression for the magnetic flux through the loop at time t.
(b) Find an expression for the magnitude of the induced EMF in the loop at time t.

Answer 1

a) Magnetic Flux = Dot product of Magnetic Field Vector and Area Vector

=> Flux = <b>B</b> * <b>A</b>
= BAcosθ

At time t, θ = θ(0) + wt
= (2/π) + 60t

Plug this value into the equation for flux.

Answer 2

b) Induced EMF = -(Rate of change of Flux / time)

Differentiate the flux function with respect to t, to obtain the expression.

Note that the negative sign indicates that the EMF is induced in the opposite direction, as per Lenz's Law.

Answer 3

Let us know if you do not know what "differentiate" means. There is another way.

Answer 4

Thank you both, I understand differentiation however I would be interested to see the other way for completeness should you have time.

My only question is how would I best relate the R for resistance to the magnetic flux equation would I be using faradays law here?