There are two current carrying planar coils made each from identical wires of length L. `C_1` is circular (radius R) and `C_2` is square (side a). They are so constructed that they have same frequency of oscillation when they are placed in the same uniform `vec B` and carry the same current. Find a in terms of R .

Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is

Two circular coils are made of two identical wires of same length and carry same current. If the number of turns of the two coils are 4 and 2, then the ratio of magnetic induction at the centres will be

A circular coil of radius R carries a current i . The magnetic field at its centre is B . The distance from the centre on the axis of the coil where the magnetic field will be B//8 is

Two metallic spheres of radii R and 2R are charged so that both of these have same surface charge density sigma . If they are connected to each other with a conducting wire, in which direction will the charge flow and why?

Two identical coils each of radius r and having number of turns n are lying in perpendicular planes such that they have common centre. Find the magnetic field at the centre of the coils if they carry currents equal to I and sqrt31 respectively.

Two uniform brass rods A and B of length l and 2l and radii 2r and r respectively are heated to the same temperature. The ratio of the increase in the volume of A to that of B is

Two metallic spheres S_1 and S_2 are made of the same material and have got identical surface finish. The mass of S_1 is thrice that of S_2 . Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. the ratio of the initial rate of cooling of S_1 to that of S_2 is

A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, R is equal to

Two concentric circular coils of five turns each are situated in the same plane. Their radii are 20 cm and 30 cm and they carry respectively 0.2 A and 0.3 A current in same direction. The magnetic field in tesla at the centre is

A conductor has 3 segments two straight and of length L each and a semicircular with radius R. It carries a current I. What is the magnetic field B at point P