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Physics Question on Magnetism and Maxwell's Equations

A circular loop of wire with radius R is centered at the origin of the xy-plane. The magnetic field at a point within the loop is, B→(ρ,ϕ,z,t)=kρ3t3z^\overrightarrow B(\rho,\phi,z,t)=k\rho^3t^3\hat{z}, where k is a positive constant of appropriate dimensions. Neglecting the effects of any current induced in the loop, the magnitude of the induced emf in the loop at time t is

A

6πkt2R55\frac{6\pi kt^2R^5}{5}

B

5πkt2R56\frac{5\pi kt^2R^5}{6}

C

3πkt2R52\frac{3\pi kt^2R^5}{2}

D

πkt2R52\frac{\pi kt^2R^5}{2}

Answer

6πkt2R55\frac{6\pi kt^2R^5}{5}

Explanation

Solution

The correct answer is (A) : 6πkt2R55\frac{6\pi kt^2R^5}{5}