QUESTIONS

Write expression for the magnetic field due to an infinitely-long current-carrying straight conductor.

The figure shows two semicircular current-loops of radii $a_1$ and $a_2$. Find the magnitude and direction of the magnetic field at the common centre O.

An electron moving with velocity $5.0\times {10}^7 {\mathrm{ms}}^{-1}$ enters a magnetic field of $1.0 \mathrm{N} {\mathrm{A}}^{-1} {\mathrm{m}}^{-1}$ at an angle of $30°$ to the field. Calculate the force on the electron.

A current of $5.0 \mathrm{A}$ is flowing upwards in a long vertical wire placed in a uniform horizontal northward magnetic field of $0.020 \mathrm{T}$. How much force and in what direction will the field exert on $0.06 \mathrm{m}$ length of the wire?  

A long horizontal rigidly supported wire carries a current of$100 \mathrm{A}$. Directly above it and parallel to it is a fine wire that carries a current of $200 \mathrm{A}$ and weighs$0.05 \mathrm{N}/\mathrm{m}.$ How far above the lower wire should the fine wire be kept to support it by magnetic repulsion?

Two very long, straight, parallel wires $\mathrm{A}$ and $\mathrm{B}$ carry currents of $10 \mathrm{A}$ and $20 \mathrm{A}$ respectively and are at a distance $20 \mathrm{cm}$ apart. If a third wire $\mathrm{C}$ (length $15 \mathrm{cm}$) having a current of $10 \mathrm{A}$ is placed between them, how much force will act on $\mathrm{C}$? The direction of current in all the three wires is same.

Calculate the magnetic field in which the cyclotron dees should be placed to accelerate protons. The applied frequency is $8$ megacycles/second. Take proton mass $1.67 \mathrm{x} {10}^{-27} \mathrm{kg}.$

A cyclotron accelerating protons has dees of $0.4 \mathrm{m}$ radius and a radio-frequency supply of $12$ megacycles/ second at $2000$ volt maximum value. Calculate the magnitude of the required magnetic field, the energy and velocity acquired by the protons. Take proton mass$1.67 x {10}^{27} \mathrm{kg}.$