Question

The magnetic flux $\varphi$ linked with a coil depends on time t as $\varphi =a{t}^n$ , where a and n are constants. The emfinduced in the coil is e

• A. If 0 < n < 1, e = 0
• B. If 0 < n < 1, e $\ne$ 0
• C. If n = 1, e is constant
• D. If n > 1, |e| increases with time

Answer 1

Answer: (B), (C), (D)

The correct options are
B If 0 < n < 1, e $\ne$ 0
C If n = 1, e is constant
D If n > 1, |e| increases with time

$|E_{in}|=|e|=\frac{d\varphi }{dt}\Rightarrow |e|=na{t}^{n-1}$

If 0 < n < 1 $\Rightarrow$ (n - 1) negative $\Rightarrow |e|=\frac{na}{t^{1-1}}$ hence |e| decay with time.

If n = 1 $\Rightarrow$ = na = constant; If n > 1 $\Rightarrow$ |e| increases with time.