Electricity and Magnetism Answers

A parallel-plate capacitor has plates with
area of cross-section 100 cm² and separated
by 1.0 cm. A potential difference of 100 V
is applied when no dielectric is present. A
dielectric slab of relative permittivity 5 and
thickness 0.5 cm is introduced between the
plates. Calculate the free charge on the
capacitor plates.

Show that the frequency of an electromagnetic wave undergoing reflection and transmission at an interface of two dielectrics remains invariant.

The electric field in a certain region is given
by E = 100 k . How much flux passes
through an area A if it is a portion of
i) the xy plane,
ii) the xz plane,
iii) the yz plane ?

Using Gauss' law in electrostatics, prove
that the charge resides only on the surface
of a conductor.

The electric potential at any point is given
by ¢= xy(z²— 3xy). Calculate the electric field E at that point.

Two point charges are 5 m apart and their
combined charge is 100 uC. If one repels
the other with a force of 0.9 N. Calculate
their values.

Two point changes +q and -q are separated by distance d .A particular electric field line emanating from charge +q at an angle of 60° with horizontal line attains maximum in height h above line AB join charges +q and -q on horizontal plane. IF h = ((√x.)(d))/6, then find the value of x.

The quality factor of a weakly damped
oscillator of frequency 200 Hz is 1000.
Calculate the time in which its energy
becomes 20% of the initial value.

Two oscillations along the same line are
described by the equations
x1= 0.03 cos (10π t)
and x2= 0.03 cos (12π t)
Obtain the equation describing the resultant
motion due to superposition of these two
oscillations.

A proton a deuteron (nucleus of a deuterium atom) and an alpha particle having the same kinetic energy are moving in circular trajectories constant magnetic field. If our R1, R2 and R3 denote respectively the radius of trajectories of these particles then show the relationship between the three.