Electricity and Magnetism Answers

An atom of atomic number Z has a nuclear charge Z_e and Z electrons

revolving around it. As a model of this atom, consider the nucleus as a point

charge and treat the electron cloud as a total charge- Z_e distributed uniformly

throughout a sphere of radius r_o. When an external field E is applied, the

nucleus is displaced an amount x. Show that a restoring force x(Ze)²/4Pir³_oE_o

is produced and must be equal to ZeE. Thus show that the induced dipole moment is p =4*Pi*E₀r₀³E and is linearly related to E.

if the conduction current density J=5sin(wt-20z)ay +cos(wt-20z)az mA/m^2 then evaluate the volume charge density

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A circular current–carrying coil has a radius R. Determine the distance in terms of R, of a point on the axis from the centre of the coil where the magnetic field produced by the coil is 1/8 of its value at the centre of the coil.

A long straight copper wire of radius R carries a free current I. The current is distributed uniformly over the cross-section of the wire. Find the magnetizing field H outside and inside the wire

 A rectangular loop of conducting wire with sides 3.0 m and 1.0 m is perpendicular to a uniform magnetic field The magnitude of the magnetic field varies with time as B = 0.08 + 0.75 t, where B is in Teslas and t is in seconds. A battery of 12.0V and negligible resistance is connected in the loop as shown in the figure. (a) Determine the total emf in the circuit. (b) What is the direction of the current through the circuit? 19. What inductance will be needed to store 1.00 Wh of energy in a coil carrying a current of 20 A?

 A long thin solenoid has radius 2.40 cm and 1000 turns per meter. The current in the solenoid is increasing at a constant rate of 50.0 A/s. Determine the magnitude of the induced electric field at a point inside the solenoid and 0.80 cm from the axis of the solenoid.

 Show that the continuity equation follows from Maxwell's equations.