Electricity and Magnetism Answers

Two thin, spherical, concentric metal shells have a radius of 6 cm and 8 cm. The inner shell carries a charge of 7 nC and the outer shell carries a charge of 4 nC. Find the resulting electric field at a) 7 cm from the centre; b) 10 cm from the centre.

At 12 cm in the radial direction from a conductive sphere of radius 10 cm, the electric field is 1800 N/C and its orientation points towards the interior of the sphere. Find the surface density of the charge on the sphere.

Four point charges (two with q=2.50µC and two with q=-3.0µC) are situated at the corners of a square of a side 1.0m. Find the resultant force that the charge at A will experience due to charges at the corners of the square and it’s direction.

(this question had a diagram but the diagram looks like a square, qA is in the top left corner, qB is in the top right corner. -qC is in the bottom corner of left and -qD is in the bottom corner of right.)

A plane wave traveling along the x-axis in a polystyrene-filled region with 𝜀𝑟 = 2.54 has an electric field given by 𝐸𝑦=𝐸0cos(𝜔𝑡−𝑘𝑥). The frequency is 2.4 GHz, and 𝐸0= 5.0 V/m.

Find the following:

1.1.1. The amplitude and direction of the magnetic field;

1.1.2. The phase velocity;

1.1.3. The wavelength; and

1.1.4. The phase shift between the positions 𝑥1=0.1𝑚 and 𝑥2=0.15𝑚

A copper microstrip transmission line is to be designed for a 100 Ω characteristic impedance. The substrate is 0.51 mm thick, 𝜀𝑟 = 2.2 and tan δ = 0.001.

At 5 GHz, find:

3.1.1. The guide wavelength on the line (in cm) and;

3.1.2. The total attenuation in dB/cm.

A circular copper waveguide has a radius of 0.4 cm and is filled with a dielectric material having 𝜀𝑟 = 1.5 and tan δ = 0.0002.

2.1.1. Identify the first four propagating modes and their cut-off frequencies.

2.1.2. For the dominant mode, calculate the attenuation due to dielectric loss and attenuation due to conductor loss at 20 GHz.

A plane wave traveling along the x-axis in a polystyrene-filled region with 𝜀𝑟 = 2.54 has an electric field given by 𝐸𝑦=𝐸0cos(𝜔𝑡−𝑘𝑥). The frequency is 2.4 GHz, and 𝐸0= 5.0 V/m.

Find the following:

1.1.1. The amplitude and direction of the magnetic field;

1.1.2. The phase velocity;

1.1.3. The wavelength; and

1.1.4. The phase shift between the positions 𝑥1=0.1𝑚 and 𝑥2=0.15𝑚

Three charged spheres are at the positions shown in the figure.

(a) Find the net electrostatic force at sphere B.

(b) Find the net electric field at (4,-3)

A point charge of 16 uc is placed in the centre of a conductive shell carrying a charge of -8 uc. What are the charges on the inner and outer surfaces of the shell?

A spherical conductor of radius 8 cm has a uniform surface charge density of 0.1 nC/m^2. Determine the electric field: a) on the surface of the conductor; b) at a distance of 10 cm from the centre of the conductor.