A proton goes undeflected in a crossed electric and magnetic field (the fields are perpendicular to each other) at a speed of ${10}^5 \mathrm{m}/\mathrm{s}$. The velocity is perpendicular to both the fields. When the electric field is switched off, the proton moves along a circle of radius $2 \mathrm{cm}$. Find the magnitudes of the electric and the magnetic fields. Take the mass of the proton $= 1.6 \times {10}^{–27} \mathrm{kg}$.

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.

A wire carrying a current $i$, is kept in the $x-y$ plane along the curve $y=A\sin \left(\frac{2\mathrm{\pi }}{\lambda }x\right)$. A magnetic field $B$ exists in the $z$-direction. Find the magnitude of the magnetic force on the portion of the wire between $x=0$ and $x=\lambda$.

A rigid wire consists of a quarter-circular portion of a circle of radius $R$ and two straight sections (figure). The wire is partially immersed in a perpendicular magnetic field $B$ as shown in the figure. Find the magnetic force on the wire if it carries a current $\mathrm{i}$.