Question

The magnetic flux ϕ , through a stationary loop of wire, having a resistance R, varies with time as ϕ = (at² + bt) where a and b are positive constants. The average emf, and the total charge flowing in the loop in the time interval t = 0 to t = \(\tau\) , would be equal, respectively, to

(1) \((a\tau +b),(\frac{a\tau ^2+b \tau}{R})\)

(2) \((a\tau +b),(\frac{a\tau ^2+b \tau}{2R})\)

(3) \((\frac{a\tau +b}{2}),(\frac{a\tau ^2+b \tau}{R})\)

(4) \(2(a\tau +b),(\frac{a\tau ^2+b \tau}{2R})\)

Answer 1

We have |ε| = \(\frac{dϕ}{dt}=2at+b\)