Physics

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The current in a very long, tightly wound solenoid with radius a and n turns per munit length varies in time according to the equation i(t)=Ct^2, where the current i is in amps and the time t is in seconds, and C is constant with appropriate units. Concentric with the solenoid is a conducting ring of radius r.
a) Write an expression for the potential difference induced in the ring.

b) Write an expression for the magnitude of the electric field induced at an arbitrary point of the ring.

c) Is the ring necessary for the induced electric field to exist?

a) I think that the area is n*pi*r^2 and that the magnetic field mu_naught *n*i
so I'm not sure if that makes the expression: Vind=N*pi*r^2*cos(theta)d/dt(mu_naught*n*i)
b) the same thing as B (assuming I have b correct) times v. The image says V=V(t) but I'm not sure what they are referring to.

c) I suppose...

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