Electricity and Magnetism Answers

Using Stoke’s Theorem evaluate the line integral ∫ ↓c F. dl where C is the ellipse

x²/4 +y²/16 = 1 in the xy - plane and F vector = 2x²i^ +4xj^ +2z²k^.

A dielectric object is placed in an electric field. The object becomes polarised and

a large number of atomic/molecular dipoles in the object align in the direction of the applied electric field. Derive an expression for the electric potential due to this polarised dielectric at a point outside the dielectric.

The expression of the electric field associated with an electromagnetic wave in vacuum is given by

E vector =(200Vm^-1) x^ . sin(2π×10^8 t -ky)

Determine the the direction of propagation, wave number, frequency, and the

magnitude and direction of the magnetic field associated with the wave.

Discuss Maxwell’s generalisation of Ampere’s law.

A time varying magnetic field B(t) = B↓0 cosωt pointing out of the page fills the

region enclosed by a circle of radius a shown in the figure below. Determine the

induced electric field.

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In the Bohr model of hydrogen atom, the electron follows a circular orbit centred on

the nucleus containing a proton. The motion of the electron along the circular orbit

constitutes a current. Calculate the magnetic field produced by the orbiting electron

at the site of the proton.

A sphere of radius R carries a charge of volume charge density ρ= ar, where a is a

constant and r denotes the distance from the centre of the sphere. Calculate the

total charge enclosed by the sphere and the electric field at points lying inside and

outside the sphere.

Two electric charges 2 µC and –1 µC are placed at a distance of 20 cm from each

other in vacuum. Locate the point on the line joining these two charges outside the

region between them at which the electric potential is zero with reference to the

positive charge.

a charge of 20 x 10-6 c is 20 cm from another charge of 60 x 10-6 c. (b) determine the ep midway between them.