Find an expression for the magnetic flux through the loop, in terms of the symbols above and appropriate constants, then evaluate the magnetic flux at time t = 25.0 s.

Consider a circular loop of wire, of resistance R = 12.5Ω and radius r = 5.00 cm, which is

placed with its normal initially at an angle θ = 45.0◦ to a magnetic field of magnitude B(t),

which always points in a certain fixed direction. The magnetic field is uniform but not static;

that is, at any particular instant, the magnetic field has the same strength at all points

(uniform), but that the uniform field strength changes with time (non-static). In particular,

the magnetic field strength at time t is given by B(t) = B0 exp(kt) where B0 and k are

constants with values of 6.00 × 10−2T and 0.125 s−1 respectively.

(a) Find an expression for the magnetic flux through the loop, in terms of the symbols above

and appropriate constants, then evaluate the magnetic flux at time t = 25.0 s.

(b) Find an expression for the magnitude of the induced EMF in the loop of wire, in terms of

the symbols above and appropriate constants, then determine the time at which the induced

EMF has a value of 2.50V.

(c) Find an expression for the magnitude of the induced current in the loop of wire, in terms

of the symbols above and appropriate constants. For the current in the wire at time

t = 50.0 s to be the same as the current in the wire at time t = 25.0 s (as in (a)), to what

angle must the value of θ be changed?