Electromagnetic...

Three resistance of magnitude $$R$$ each are connected in the form of an equilateral triangle of side $$a$$. The combination is placed in a magnetic field $$B=B_{0}e^{-\lambda t}$$
perpendicular to the plane. The induced current in the circuit is given by:

Consider the situation shown in figure. If the closed loop is completely enclosed in the circuit containing the switch, the closed loop will show____

A wire is sliding as shown in the figure. The angle between the acceleration and velocity of the wire is

A solenoid of inductance $$L$$ and resistance $$r$$ is connected in parallel to a resistance $$R$$ and a battery of emf $$E$$. Initially if the switch is closed for a long time and at $$t=0$$, then the :

An Indian ship with a vertical conducting mass navigates the Indian ocean in the latitude of magnetic equator. To induce the greatest emf in the mast, the ship should proceed:

A short solenoid (length $$l$$ and radius $$r$$, with $$n$$ turns per unit length) lies well inside and on the axis of a very long, coaxial solenoid (length $$L$$, radius $$R$$ and $$N$$ turns per unit length, with $$R > r$$). Current $$I$$ flows in the short solenoid. 

In fig a square loop PQRS of side a and resistance r is placed neat an infinitely long wire carrying a constant current l. the sides PQ and Rs parallel to the wire. The wore and the loop are in the same plane. The loop is rotated $$180^{\circ}$$ about an axis parallel to the long wire and passing through the mid-points of the sides QR and PS.The total amount of charge which passes through any point of the loop during rotation is 

A metal bar is moving with a velocity of $$v=5 cm s^{-1}$$ over a U-shaped conductor.AT $$t=0$$, the external magnetic field is 0.1 T directed out of the page and is increasing at a rate of  $$0.2 T s^{-1}$$. Take $$l= 5 cm$$ and $$ t=0, x=5 cm$$

The current flowing in the circuit is 

An aircraft is flying at a level height in presence the magnetic field of the Earth. If an electric bulb is connected between the two extreme ends of the wings,

The radius of the circular conducting loop shown in fig. is R. Magnetic field is decreasing at a constant rate $$\alpha$$ Resistance per unit length of the loop is $$\rho$$then the current in wire AB is (AB is one of the diameter)