Two magnets $A$ and $B $ are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point $P$ which gets deflected through an angle $\theta $ under the influence of magnets. The ratio of distance ${d_1}$ and ${d_2}$ will be
${(2\tan \theta )^{1/3}}$
${(2\tan \theta )^{ - 1/3}}$
${(2\cot \theta )^{1/3}}$
${(2\cot \theta )^{ - 1/3}}$
Verify the Gauss’s law for magnetic field of a point dipole of dipole moment ${{\rm{\vec m}}}$ at the origin for the surface which is a sphere of radius $\mathrm{R}$.
Write the Gauss’s law in equation form for electrostatics and magnetism. What is the difference between them ?
Two lines of force due to a bar magnet
Two similar bar magnets $P $ and $Q$ , each of magnetic moment $M,$ are taken, If $P$ is cut along its axial line and $Q$ is cut along its equatorial line, all the four pieces obtained have
$(a)$ What happens if a bar magnet is cut into two pieces: $(i)$ transverse to its length, $(ii)$ along its length?
$(b)$ A magnetised needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet, however, experiences a force of attraction in addition to a torque. Why?
$(c)$ Must every magnetic configuration have a north pole and a south pole? What about the field due to a toroid?
$(d)$ Two identical looking iron bars $A$ and $B$ are given, one of which is definitely known to be magnetised. (We do not know which one.) How would one ascertain whether or not both are magnetised? If only one is magnetised, how does one ascertain which one? [Use nothing else but the bars $A$ and $B$.]