Magnetism and M...

The potential energy stored in the magnetic field inside the given section of the co-axial cylinder is given by the expression. (by integration of the energy density of the magnetic field over the volume of the section enclosed between the cylindrical shells)?

A metal wire of mass $$m$$ slides without friction on two rails at distance $$d$$ apart. The track is in a vertical uniform field of induction $$\vec B.$$ A constant current $$\vec i$$ flows along one rail across the wire and back down the other rail the velocity of the wire as a function of time, assuming it to be at rest initially.

Write the dimension of the magnetic flux in terms of mass, time, length and charge.

There are two current carrying planar coils each made from identical wires of length L. $$C_1$$ is circular (radius R) and $$C_2$$ is square(side a). They are so constructed that they have same frequency of oscillation when they are place in the same uniform magnetic field $$\vec{B}$$ and carry the same current. Find a in terms of R.

If $$M_2$$ = magnetization of a paramagnetic sample, B = external magnetic field, T = absolute temperature, C = curie constant then according to Curie's law in magnetism, the correct relation is

Statement-1: The core of the transformer is laminated to avoid loss of energy.
Statement-2: A laminated metal sheet placed in a changing magnetic field has lower eddy current.

An electron in the ground state of hydrogen atom is revolving in anticlockwise direction in a circular orbit of radius $$R$$.
Obtain an expression for the orbital magnetic moment of the electron.

As shown in the figure, four identical loops are placed in a uniform magnetic field B. The loops carry equal current i. $$\hat{n}$$ denotes the normal to the plane of each loop. Potential energies in descending order are.

A domain in ferromagnetic iron is in the form of a cube of side length $$2$$ $$\mu m$$ then the number of iron atoms in the domain are (Molecular mass of iron $$=55$$g $$mol^{-1}$$ and density $$=7.92$$g $$cm^{-3}$$)

A short bar magnet of magnetic moment m= $$0.32JT^1$$ is placed in a uniform magnetic field of $$0.15 T$$. If the bar is free to rotate in the plane of the field, which orientation would correspond to its (a) stable, and (b) unstable equilibrium? What is the potential energy of the magnet in each case?