Question 1:
moderateTwo particles, each of mass m and charge q, are attached to the two ends of a massless rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is :
Question 2:
moderateA magnetic substance has susceptibility –0.05 at 300 K. The magnetic susceptibility of the substance at 600 K will be :
Question 3:
moderateTwo circular coils 1 and 2 are made from the same wire but the radius of the 1st coil is twice that of the 2nd coil. What is the ratio of potential difference applied across them so that the magnetic field at their center is the same?
(2006)
Magnetic field $B = \frac{\mu_0 N I}{2 R}$. Since $B$ and length of wire are same, $N_1 R_1 = N_2 R_2$. With $R_1 = 2R_2$, $N_1 = N_2 / 2$. The potential difference ratio $\frac{V_1}{V_2} = \frac{I_1 R_{\text{wire}, 1}}{I_2 R_{\text{wire}, 2}} = 4$.
Question 4:
moderateA coil in the shape of an equilateral triangle of side $L$ is suspended between the pole pieces of a permanent magnet such that $B$ is in plane of the coil. If due to a current $i$ in the triangle a torque $tau$ acts on it, the side $L$ of the triangle is :
(2005)
The magnetic moment is $M = i A = i \left( \frac{\sqrt{3}}{4} L^2 \right)$. The torque is $\tau = M B = i \frac{sqrt{3}}{4} L^2 B$. Solving for $L$ yields $2 \left[ \frac{\tau}{\sqrt{3}Bi} \right]^{1/2}$.