# Thread: Varying current in a solenoid

1. 1)When the current through a solenoid increases at a constant rate, the induced current:
a)is a constant and is in the direction of the inducing current
b)is a constant and is opposite to the direction of the inducing current
c)increases with time and is in the direction of the inducing current
d)increases with time and is opposite to the direction of the inducing current

I solved it in the following way:

For a solenoid,
(phi) = ki {phi = Flux linked with the solenoid}
Where k = [(mu)x(pi)x(Nxa)]/2
d(phi)/dt = kx(di/dt)
e = kx(di/dt) {Here e = induced e.m.f}
iR = kx(di/dt)
(R/k)dt = di/i
Integrating we get,
(Rt)/k = log(i)

i = 10^[(Rt)/k]
i = 10^[(Rt)/k]
So, the current increases with time. In the above solution I have taken e as positive because then only I get the book answer. Please guide me.  2.

3. your answer contradicts lenz's law - the induced EMF (and thus current) always opposes the change that created it (thus conserving energy)  Bookmarks
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