An electron gun $\mathrm{G}$ emits electron of energy $2 \mathrm{keV}$ travelling in the positive $x-$direction. The electrons are required to hit the spot $S$ where $\mathrm{GS}=0.1 \mathrm{m}$ and the line $\mathrm{GS}$ makes an angle of $60°$ with the $x-$axis, as shown in the figure. A uniform magnetic field $B$ parallel to $\mathrm{GS}$ exists in the region outside of electron gun. Find the minimum value of $\mathrm{B}$ needed to make the electron hit $\mathrm{S}$. [Take mass of electron $= 9 \times {10}^{–31} \mathrm{kg}$]

 

A conducting wire of length $\mathcal{l}$, lying normal to a magnetic field $B$, moves with a velocity $v$ as shown in figure (a). Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons concentrate at one end resulting in an electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when the redistribution stops. (c) What potential difference is developed between the ends of the wire?

A current of $2 \mathrm{A}$ enters at the corner d of a square frame $\mathrm{abcd}$ of side $10 \mathrm{cm}$ and leaves at the opposite corner $b$. A magnetic field $B=0.1 \mathrm{T}$ exists in the space in direction perpendicular to the plane of the frame as shown in figure. Find the magnitude and direction of the magnetic forces on the four sides of the frame.

A magnetic field of strength $1.0 \mathrm{T}$ is produced by a strong electromagnet in a cylindrical region of diameter $4.0 \mathrm{cm}$ as shown in figure. A wire, carrying a current of $2.0 \mathrm{A}$, is placed perpendicular to and intersecting the axis of the cylindrical region. Find the magnitude of the force acting on the wire.