Let us consider two solenoids $$A$$ and $$B$$, made from same magnetic material of relative permeability $$\mu_r$$ and equal area of cross-section. Length of $$A$$ is twice that of $$B$$ and the number of turns per unit length in $$A$$ is half that of $$B$$. The ratio of self inductances of the two solenoids, $$L_A: L_B$$ is

An emf is generated by an ac generator having 100 turn coil, of loop area $$1 \mathrm{~m}^2$$. The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of $$0.05 \mathrm{~T}$$ perpendicular to the axis of rotation of the coil. The maximum value of emf is :-

The net magnetic flux through any closed surface is :

The magnetic flux linked to a circular coil of radius R is

$$\phi = 2{t^3} + 4{t^2} + 2t + 5$$ Wb

The magnitude of induced emf in the coil at t = 5 s is