Electricity and Magnetism Answers

The electric field intensity due to point charge can be written as: &  . Discuss the difference between these two equations.                                     

A hollow rectangular waveguide has dimensions a = 2.28 cm., b = 1.01 cm. What TE modes will propagate in this waveguide if the frequency of the electromagnetic waves is 1.7 x 1010 Hz? What range of frequencies can be used to excite only one TE mode?

Show that the wave number of an electromagnetic wave plane wave is complex in a material with conductivity

Find the magnetic force experienced by an electronic of charge 1.6 x 10^-19 prejected into a magnetice field dentist iot , with a velocity of 3 x 10⁹ in a direction

Parallel time the field

At right angle to the field

At angle 30⁰ to the field

Show that the wave number of an electromagnetic wave plane wave is complex in a material with conductivity 𝜎. Assume the wave is propagating along the y-axis. Determine the real and imaginary parts of the wave number in terms of 𝜔, 𝜇, 𝜀 and �

 State Maxwell’s equation for the curl of the magnetic and the electric field in free space. State the meaning of all the terms in the equations and identify the displacement current density. Using Maxwell’s equations, derive the wave equations for B. Show that the wave equations admit plane waves for the electric and magnetic fields in free space of the form 𝑬 = 𝑬𝟎𝑒 𝑖(𝑘𝑧−𝜔𝑡) , 𝑩 = 𝑩𝟎𝑒 𝑖(𝑘𝑧−𝜔𝑡) where 𝑬𝟎 and 𝑩𝟎 are constant vectors with real components if 𝑘 2 = 𝜔 2𝜇0𝜀0. Show that E and B are transverse waves propagating with speed 𝑐 = 3 × 10^8 ms-1 . 

A point charge of +10-7C is situated at the centre of a cube of side 1 m. Calculate the electric flux through the surface of the cube

A square loop in a magnetic field B

1) (i) State Faraday’s law of electromagnetic induction for the induced e.m.f. in a circuit due to changing magnetic flux.

(ii) Assume the axis of the loop is along the x-axis and the loop rotates in a clockwise direction with angular speed

protons of k.e 10^12 are injected into a uniform magnetic field of strength 10 Tesla .A magnetic field exists only inside the cylindrical region of diameter 50 cm and is parallel to the axis of cylinder at the point of injection. The proton beam is directed towards the axis of the cylinder and is perpendicular to it . By the time the beam exists the magnetic field changes direction by