Questions in Moving Charges and Magnetism

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In the figure, the magnetic induction at O due to the whole length of the conductor is Question Image
In the figure shown there are two semicircles of radii ${r_1}$ and ${r_2}$ in which a current i is flowing. The magnetic induction at the centre O will be Question Image
The magnetic moment of a current carrying loop is $2.1 \times {10^{ - 25}}\,amp \times {m^2}$. The magnetic field at a point on its axis at a distance of $1\,{\AA}$ is
Two straight horizontal parallel wires are carrying the same current in the same direction, $d$ is the distance between the wires. You are provided with a small freely suspended magnetic needle. At which of the following positions will the orientation of the needle be independent of the magnitude of the current in the wires
A particle carrying a charge equal to 100 times the charge on an electron is rotating per second in a circular path of radius 0.8 metre. The value of the magnetic field produced at the centre will be (${\mu _0} = $ permeability for vacuum)
A circular coil of radius R carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance r from the centre of the coil, such that r>>R, varies as
In hydrogen atom, an electron is revolving in the orbit of radius $0.53\,{\AA}$ with $6.6 \times {10^{15}}$ rotations/second. Magnetic field produced at the centre of the orbit is
The magnetic induction due to an infinitely long straight wire carrying a current i at a distance r from wire is given by
Magnetic effect of current was discovered by
Two concentric circular coils of ten turns each are situated in the same plane. Their radii are $20$ and $40 cm$ and they carry respectively $0.2$ and $0.3 ampere$ current in opposite direction. The magnetic field in $weber/{m^2}$ at the centre is

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