As shown in figure a cell is connected across two points A and B of a uniform circular conductor of radius r. Prove that the magnetic field induction at its centre O will be zero.

Two semi infinitely long straight current carrying conductors are held in the form as shown in figure. One common end of them is at the origin. If both the conductors carry same current I, find the value of the magnetic field induction at a point (a, b).

An infinitely long conductor as shown in figure, carrying a current I with a semicircular loop on X-Y plane and two straight parts, one parallel to X-axis and another coinciding with Z-axis. What is the magnetic field induction at the centre C of the semi-circular loop.

A metallic wire carrying a current I is bent into the form as shown in the figure. The circular portion ABC of the wire is of radius r and the straight portion AC subtends an angle 2theta at the centre O. Find the magnetic field due to the conductor at point O. If the radius of the curved path is r, find the magnetic field at the centre O.

An electron revolves in a circular orbit of radius r with uniform angular speed omega . From the expression for magnetic field due to current carrying circular conductor, deduce the expression for magnetic field at the center of electron orbit.

The magnetic field due to a current carrying loop of radius 3 cm at a point on axis at a distance of 4 cm from its centre of 54 mu T . Then , the value of the magnetic field at the centre of the loop is

The current that flows through a conductor of length 10 cm bent into the form of an arc of circle of radius 2 cm to produce a magnetic field of 0.1 oersted at its centre is

The question given below consist of an assertion (A) and a reason ( R). Use the following key to choose the appropriate answer to these questions from the codes (a), (b), ( c) and (d) given below: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is NOT the correct explanation of A. (c) A is true but R is false. (d) A is false and R is also false. Assertion: Magnetic lines cannot start from one point nor end at a point. Reason: The line integral of magnetic field induction over a closed path is not zero.

State the Biot-Savart's law for the magnetic field due to a current carrying element. Use this law to obtain a formula for magnetic field at athe centre of circular loop of radius r carrying steady current I . Sketch the magnetic field lines for a current loop clearly indicating the direction of the field.

Two circular coils 1 and 2 are made from the same wire but the radius of the 1st coil is twice that of the 2nd coil. What is the ratio of potentail difference applied across them so that the magnetic field at their centres is the same?