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Electromagnetism Answers

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Show that the function
i) u(x,t) = A(x + ct)³ is a solution of the one-dimensional wave equation.
ii)u(x ,t) = e^(−µt) sin x is a solution of the one-dimensional heat equation.
A long straight wire of radius 5.0 mm carries a current of 20 A. Calculate the magnetic field at the surface of the wire.Calculate the perpendicular distance from the axis of the wire at which he
magnitude of the magnetic field will be half of its value at the wire surface.
in case of A.C , the current leads voltage by 90 degree in CAPACITOR. what does this mean?
is it mean that current goes first followed by voltage
The primary turns of a transformer is 30 turns and its secondary turns is 300.if the voltage input is 24v,how much is the output?
An electron is constrained to the central axis of a ring of charge 1
coulomb and of radius 1 meter. The electrostatic force exerted on the
electron can cause the electron to oscillate through the center of the
ring. Find the frequency of small oscillation of the electron in Hertz.
derive the resonance condition for nuclear magnetic resonance.calculate the require magnetic field strength at which proton spin comes into resonance with 500 MHz radiation
Does megnetic circuit consume energy ? Why it is consume energy ?
An electron orbiting the nucleus of an atom produces tiny electric current. So why an atom does not shock anyone?

1. Fringing decreases the flux density in the air gap. how?
2. Air-gap flux is termed as usefùl flux. Why?
3. The relative permeability of a magnetic material changes with flux density. Why?
4. Does a magnetic circuit consume energy? Why’?
5. In a magnetic circuit,which part (iron or air) requires most of the ampere-turns to set up flux, tell why ?
6. In all the magnetic circuits, leakage flux exists. Why?

A non-conducting spherical shell, with an inner radius of R1 and an outer radius of R2, has carge spread non-uniformly through its volume between its inner and outer surfaces, where the volume charge density r is given by r=k/r with the distance r frome the center of the shell and a constant k.
(a) Find the net charge Q of the shell
(b) Calculate the electric field E at a distance R frome the center over the range 0 £R£¥
(c) Fin the maximum E.