Questions in Moving Charges and Magnetism

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A long solenoid has a radius $a$ and number of turns per unit length is $n$. If it carries a current $i$, then the magnetic field on its axis is directly proportional to
A cell is connected between two points of a uniformly thick circular conductor. The magnetic field at the centre of the loop will be(Here ${i_1}$ and ${i_2}$ are the currents flowing in the two parts of the circular conductor of radius $a$ and ${\mu _0}$ has the usual meaning)
A long solenoid is formed by winding 20 turns/cm. The current necessary to produce a magnetic field of 20 millitesla inside the solenoid will be approximately$(\frac{{{\mu _0}}}{{4\pi }} = {10^{ - 7}}\,tesla - metre/ampere)$
A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle $\theta $ at the centre. The value of the magnetic induction at the centre due to the current in the ring is
A current of 1 ampere is passed through a straight wire of length 2.0 metres. The magnetic field at a point in air at a distance of 3 metres from either end of wire and lying on the axis of wire will be
A long copper tube of inner radius R carries a current i. The magnetic field B inside the tube is
A straight wire of length $({\pi ^2})$ metre is carrying a current of $2A$ and the magnetic field due to it is measured at a point distant 1 cm from it. If the wire is to be bent into a circle and is to carry the same current as before, the ratio of the magnetic field at its centre to that obtained in the first case would be
The direction of magnetic lines of forces close to a straight conductor carrying current will be
If the strength of the magnetic field produced 10cm away from a infinitely long straight conductor is ${10^{ - 5}}\,Weber/{m^2}$, the value of the current flowing in the conductor will be
Due to 10 ampere of current flowing in a circular coil of 10 cm radius, the magnetic field produced at its centre is $3.14 \times {10^{ - 3}}\,Weber/{m^2}$. The number of turns in the coil will be

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