EXERCISES

Two long and parallel straight wires A and B carrying currents of $8.0 \mathrm{A}$ and $5.0 \mathrm{A}$ in the same direction are separated by a distance of $4.0 \mathrm{cm}$. Estimate the force on a $10 \mathrm{cm}$ section of wire A.

A closely wound solenoid $80 \mathrm{cm}$ long has $5$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8 \mathrm{cm}$. If the current carried is $8.0 \mathrm{A}$, estimate the magnitude of $B$ inside the solenoid near its centre.

A square coil of side $10 \mathrm{cm}$ consists of $20 \mathrm{turns}$ and carries a current of $12 \mathrm{A}$. The coil is suspended vertically, and the normal to the plane of the coil makes an angle of $30°$ with the direction of a uniform horizontal magnetic field of magnitude $0.80 \mathrm{T}$. What is the magnitude of torque experienced by the coil.

Two moving coil meters, $M_{\mathrm{1}}$ and $M_{\mathrm{2}}$ have the following particulars: $R_{\mathrm{1}}=10 \mathrm{\Omega }$, $N_{\mathrm{1}}=30$, $A_{\mathrm{1}}=3.6\times {10}^{-3} {\mathrm{m}}^2$, $B_{\mathrm{1}}=0.25\hspace{0.17em}\mathrm{T}$, $R_{\mathrm{2}}=14 \mathrm{\Omega }$, $N_{\mathrm{2}}=42$, $A_{\mathrm{2}}=1.8\times {10}^{-3} {\mathrm{m}}^2$, $B_{\mathrm{2}}=0.50\hspace{0.17em}\mathrm{T}$.
(The spring constants are identical for the two meters). Determine the ratio of current sensitivity and voltage sensitivity of $M_{\mathrm{2}}$ and $M_{\mathrm{1}}$.

In a chamber, a uniform magnetic field of $6.5 \mathrm{G}$ ( $1\mathrm{G}={10}^{-4} \mathrm{T}$ ) is maintained. An electron is shot into the field with a speed of $4.8\times {10}^6 \mathrm{m}{\mathrm{s}}^{-1}$ normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit.
( $e=1.6\times {10}^{-19} \mathrm{C}, m_e=9.1\times {10}^{-31} \mathrm{kg}$)

Obtain the frequency of revolution of the electron, in a magnetic field, in its circular orbit. Does the answer depend on the speed of the electron? Explain.

 A circular coil of $30$ turns and radius $8.0 \mathrm{cm}$ carrying a current of $6.0 \mathrm{A}$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0 \mathrm{T}$. The field lines make an angle of $60°$with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.

A circular coil of $30$ turns and radius $8.0 \mathrm{cm}$ carrying a current of $6.0 \mathrm{A}$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0 \mathrm{T}$. The field lines make an angle of $60°$ with the normal of the coil. A counter torque is applied to prevent the coil from turning. Would your answer change, if the circular coil were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)