Two 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 :
The materials suitable for making electromagnets should have :
The universal property among all substances is:
A magnetic substance has susceptibility –0.05 at 300 K. The magnetic susceptibility of the substance at 600 K will be :
Magnetic susceptibility of the following is :
Diamagnetic substances characterise by :
\(\varepsilon_0\) and \(\mu_0\) are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are \(2\varepsilon_0\) and \(1.5\mu_0\) respectively, the refractive index of the medium will nearly be
The speed of light in free space is \(c = \frac{1}{\sqrt{\varepsilon_0\mu_0}}\) and in a medium is \(v = \frac{1}{\sqrt{\varepsilon\mu}}\). The refractive index \(n = \frac{c}{v} = \sqrt{\frac{\varepsilon\mu}{\varepsilon_0\mu_0}} = \sqrt{2 \times 1.5} = \sqrt{3}\).
A thin circular wire carrying a current \(I\) has a magnetic moment \(M\). The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment of:
For circle: \(M = I \pi R^2\) where \(2\pi R = L ⇒ R = \frac{L}{2\pi}\), so \(M = \frac{I L^2}{4\pi}\). For square of side \(a = \frac{L}{4}\): \(M' = I a^2 = \frac{I L^2}{16}\). Thus, \(M' = \frac{\pi}{4} M\).
The magnetic materials having negative magnetic susceptibility are:
Diamagnetic substances have negative magnetic susceptibility because they develop magnetization in a direction opposite to the applied magnetic field.
To increase the current sensitivity of a moving coil galvanometer, we should:
Current sensitivity is given by \(I_s = \frac{NBA}{C}\). To increase it, we need to increase \(N\), \(B\), \(A\) or decrease \(C\). None of the options perform these changes.