A long solenoid has n turns per unit length and radius a. A current `l = I_0` sin `omega` t flows through it. A cylindrical vessel of radius R, length L and thickness d`(dltltR)` and resistivity `rho` is kept co-axially. Find the induced current in the outer cylindrical vessel.

A fuse wire has a length l and radius r . The maximum safe current through it is

Two solenoids made of insulated conducting wires and of equal lengths are such that one is wound over another. Resistance of each of them is R and number of turns per unit lenghts is n. The solenoids are now conected in series and if current flows through them in the same direction in both cases, determine the magnetic field along the axis of solenoids in each case.

A circular loop of radius R is bent a long a diameter and given a shape as shown below. One of the semicircles (KNM) lies in XZ plane and the other one (KLM) lies in YZ plane with their centres at origin. Current l is flowing through each of the semicircles. A particle of charge q is released at the origin with a velocity oversetrarrV=-v_0uarr . Find the instantaneous force oversetrarrF on the particle. Assume the space is gravity free.

Current i_(1) and i_(2) are flowing in the same direction through tow long parallel wires kept at a distance d apart. Determine the expression for the force acting per unit length of the wires. Define 1A current from It.

A very small circular loop of radius a is initially (at t = 0) coplanar and concentric with a much larger fixed circular loop of radius b. A constant current l flows in the larger loop. The smaller loop is rotated with a constant angular speed omega about the common diameter. The emf induced in the smaller loop as a function of time t is

Two solenoids made of insulated conducting wires and of equal lengths are such that one is wound over another. Resistance of each of them is R and number of turns per unit lenghts is n. The solenoids are now connected in parallel and the combination is then connected with a battery of emf E. if current flows through them in the same direction in both cases, determine the magnetic field along the axis of solenoids in each case.

If a current passes through a metal conducting wire of area of cross section A, the drift velocity of free electrons inside the metal is v_d=1/( n e A) , where the amount of electric charge of an electron =e and the number of free electrons per unit volume of the metal=n. The applied electric field on the wire is E=V/l , where a potential difference V exists between two points, l apart, along the length of the wire. IF R is the resistance of the wire between those two points, then the resistivity of its material is rho=(RA)/l .Besides the mobility (mu) of the free electrons inside a wire is defined as their drift velocity for a unit applied electric field. Two copper wires have both lengths and radii in the ratio 1:2 if the ratio between the electric currents flowing through them is also 1:2 , what would be the ratio between the drift velocities of free electrons?

Check the correctness of the relation V=(pipr^(4))/(8etal) where V is the volume per unit time of a liquid flowing through a tube of radius r and length l, eta is the coefficient of viscosity of the liquid and p is the pressure difference between the ends of the tube.