A spatially uniform magnetic field is restricted in a circular region of space
with radius of 2.5 cm and has a constant direction; see figure below. If the
magnetic field varies with time t as B(t) = (25 mT/s^2)t^2, what is the magnitude of the induced electric field at a distance of 4.00 cm from the center of the magnetic field region at t = 2 s?
We know the magnetic flux changes from the loop is,
Now according to Faraday's law,
Now the induced electric field in the loop of radius r = 4 cm at time t = 2 s
Negative sign indicates that the induced emf oppose the change of the magnetic flux.
magnitude of the electric field,