Using Ampere.s Circuital Law, derive an expression for the magnetic field along the axis of a toroidal solenoid.

Using Ampere's circuital law, obtain an expression for the magnetic field along the axis of a current carrying solenoid of length l and having N number of turns.

Ampere's circuital law is given by

State Ampere.s circuital law.

(a)Using Ampere's circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis. (b )How is the magnetic field inside a given solenoid made strong?

Using Ampere.s circuital law, obtain an expression for the magnetic flux density .B. at a point .X. at a perpendicular distance .r. from a long current carrying conductor. (Statement of the law is not required).

Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius R . Draw the magnetic field lines due to circular wire carrying current I .

(a) Using Biot-Savart's law, derive the expression for the magnetic field in the vector form at a point on the axis of a circular current loop. (b) What does a toroid consist of? Find out the expression for the magnetic field inside a toroid for N turns of the coil having the average radius r and carrying a current I. Show the magnetic field in the open space inside and exterior to the toroid is Zero.

Using Biot-Savart’s law, derive an expression for magnetic field at any point on axial line of a current carrying circular loop. Hence, find magnitude of magnetic field intensity at the centre of circular coil.

State Biot-Savart law, giving the mathematical expression for it. Use this law to derive the expression for the magnetic field due to a circular coil carrying current at a point along its axis. How does a circular loop carrying curent behave as a magnet?

Using Gauss’ law, derive an expression for the electric field at a point near an infinitely long straight uniformly charged wire.