Magnetisation & Boundary Condition: Assignment | Electricity & Magnetism - Physics PDF Download

Q.1. A circular conductor of radius R = 1 cm has an internal field

Then find the total current in the conductor.

Q.2. The magnetic induction in vacuum at a plane surface of a uniform isotropic magnetic material is equal to B . The vector  forms an angle α with the normal to the surface. The relative permeability of the magnetic material is equal to μ . Show that the magnitude of the magnetic induction B' in the magnetic material in the vicinity of its surface is 

Thus

Q.3. A long circular cylinder of radius R carries a magnetization  where k is a constant and r is the distance from the axis; there is no free current anywhere. Find
(a) all bound currents,
(b) the magnetic field due to  for  points inside and outside the cylinder.

(a) 
Thus current has solenoidal symmetry. This is essentially a superposition of solenoids. Magnetic field is in the z -direction.
(b) From Ampere’s Law:

Q.4. At the interface between two linear dielectrics (with permeability μ₁ and μ₂), the magnetic field lines bend, as shown in the figure. Assume that there is no free current at the interface. Find the ratio

Q.5. The magnetic field in vacuum at a plane surface of a magnetic material is equal to  and the vector  forms an angle θ with the normal  of the surface. The relative permeability of the magnetic material is equal to μ. Find:
(a) The flux of the vector  through the spherical surface S of radius R, whose centre lies on the surface of the magnetic material;
(b) The circulation of the vector around the square path Γ with side ℓ located as shown in figure.

(a) 





and

Thus

(b)

Q.6. An infinitely long solid cylindrical conductor of radius r₁, carries a uniform volume current density  It is uniformly surrounded by another coaxial cylinder of a linear magnetic medium with permeability μ, up to radius r₂ as shown in the figure.

(a) Determine the magnetic field  in the region r<r₁ and magnetic induction 

 in the regions, r₁< r<r₂ and r>r₂, where r is the radial distance from the axis of the cylinder.
(b) Sketch the variation of  with r in all the three regions.

(a) Let us draw an amperian loop of radius r(r <r₁)

Similarly draw an amperian loop of radius r(r₁< r< r₂)

Again draw an amperian loop of radius r(r >r₂)


(b)

Q.7. The x - y plane is the boundary between free space and a magnetic material with relative permeability μ_r . The magnetic field in the free space is  Then find the magnetic field in the magnetic material.

The magnetic field in the magnetic material is

Q.8. A coaxial cable consists of two very long cylindrical tubes, separated by a material with susceptibility χ_m . A current I flows down the inner conductor and returns along the outer one; in each case the current distributes itself uniformly over the surface.
(a) Find the magnetic field in the region between the tubes.
(b) Find all bound currents.

(a)
(b) 

and