Electricity and Magnetism Answers

Four particles carrying charges + 2q, − 2q, + 4q and − 4q (with q = 1.0 nC) are kept at the vertices of a square of side 6.0 cm. Determine the net electric field due to these charged particles at the centre of the square. What is the electrostatic force on a particle carrying positive charge of 1.0 nC placed at the centre of the square?

A uniform plane wave of 10 kHz travelling in free space strikes a large block of a
material having ε = 9ε0, μ = 4μ0 and σ = 0 normal to the surface. If the incident
magnetic field vector is given by
B =10^− 3sin (ωt −βy) kˆ
tesla
Write the complete expressions for the incident, reflected, and transmitted field vectors.

Using Maxwell’s equations in free space, derive the wave equation for the z-component of
the electric field vector.

The volume charge density of a solid sphere of radius 0.75 m is 0.25 nCm^−3. Apply Gauss’s law to calculate the a) electric flux through the sphere and b) electric field at a distance of 1.5 m and at a distance of 0.50 m from the centre of the sphere, respectively. If this sphere were made of conducting material, what would the values of the electric fields be at these distances?

Write the plane wave form for the z-component of the electric field vector of an
electromagnetic wave of wavelength 10 cm and field strength 200 Vm–1. The wave is
propagating in the positive x-direction.

The volume charge density of a solid sphere of radius 0.75 m is 0.25 nCm^−3. Apply Gauss’s law to calculate the a) electric flux through the sphere and b) electric field at a distance of 1.5 m and at a distance of 0.50 m from the centre of the sphere, respectively. If this sphere were made of conducting material, what would the values of the electric fields be at these distances?

Three charges q, 2q and q are to be placed on a straight wire of length 10 m.
Determine the positions where the charges should to be placed so that the
electrostatic potential energy of the system is a minimum

Using Maxwell’s equations in free space, derive the wave equation for the z-component of
the electric field vector.

A uniform plane wave of 10 kHz travelling in free space strikes a large block of a
material having ε = 9ε0, μ = 4μ0 and σ = 0 normal to the surface. If the incident
magnetic field vector is given by
B =10− ^3sin (ωt −βy) kˆ
tesla
Write the complete expressions for the incident, reflected, and transmitted field vectors.

Metallic iron contains approximately 10^29 atoms per cubic meter. The magnetic moment
of each iron atom is 1.8 × 10^−23 Am−1. If all the dipoles were perfectly aligned what
would be the magnetisation M and the magnetic moment of a bar 10 cm long and 1cm^2 in
cross-section?