Electricity and Magnetism Answers

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

E = (1000 Vm^-1) z sin (2π x 10^8 t + kx)

Determine the wave number, frequency, the direction of propagation and the magnitude and direction of the magnetic field associated with the wave

Using Maxwell equation in vaccum derive the wave equation for the x component of the electric field vector associated with an electromagnetic wave

A transverse sinusoidal wave is generated at one end of a long horizontal string by a bar which moves the end up and down through a distance of 0.5cm. The motion is continuous and is repeated continuously 150 times per second.

a) If the string has a linear density of 0.25 kg.m-1 and is kept under a tension of 90N, determine the

i) speed

ii) Amplitude

iii) Frequency and

iv) Wavelength of the wave in motion

what is the expression of the medium's particle velocity as the waves pass by them

A uniform current J1 = Jocoswtêy flow on the surface z =0,and a second sheet of current J2 = J0sinwtêy flows in the surface z = pic/2w where ey is the unit vector along y and Jo,w are constant.

 a) Find solution of Maxwell's equations that fit the boundary conditions with E= B=0 z<0

 b) Calculate the flux of the poynting vector field and compare it to average power per unit area that must be supplied to drive these currents.

find the ratio of the resistances of a copper wire to an aluminum wire if the length and diameter of the aluminum wire is twice the diameter of the copper

the resistance of a rod with a length of 3.0m and a diameter of 1.0cm is 56.0 ohms. of this rod is stretched to form a wire with a diameter of 0.01cm, what is its resistance? assume that in the process of stretching the rod, its volume did not change.

wires a and b are made for the same material and have the same length. however, the diameter of wire a is thrice the diameter of wire b. wire a has a resistance of 12.0 ohms. what is the resistance of wire b?

On a plane at x = 1 the potential is V = V₀ and on a plane at x = m it is

V = Vm. Between these two planes the charge density is given as ρ=kx−1,with k > 0 being some constant. How do the potential and the electrostatic fields vary in the region between these two equipotential planes?

A linearly polarized wave with Ē in the xy plane is incident from x > 0 on an interface at x = 0. In the region x > 0 is free space and in the region x< 0 is a medium with dielectric constant e,

a) If the incidence angle is 45 degrees and angle of transmitted(refracted wave) is 90 degree find the dielectric constant ?

b)Find E and B for z>0 and calculate the time average of Poynting vector component along x (i.e. S_x) flowing through x = 0.