Two identical coils

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Two identical coils, each having

N

turns and area

A

, are mounted rigidly on a common shaft so that their planes are perpendicular to each other. The shaft rotates in a uniform magnetic field

B

with a constant angular speed

\omega

. At

t = 0

the flux through coil 1 is maximum while the flux through coil 2 is zero. (i) Write the instantaneous emf

\varepsilon_1(t)

induced in coil 1 and

\varepsilon_2(t)

induced in coil 2. (ii) When the two coils are connected in series, obtain the expression for the resultant emf

\varepsilon_{\text{total}}(t)

. (iii) Show that the peak value of

\varepsilon_{\text{total}}

\sqrt{2}\,N B A \omega

. (iv) For

N = 300

A = 25\,\text{cm}^2

B = 0.10\,\text{T}

and

\omega = 100\pi\,\text{rad\,s}^{-1}

, calculate the peak and r.m.s. values of the resultant emf.