Electricity and Magnetism Answers

For a long, straight, current-carrying conductor, use Ampere’s law to find the magnitude
and direction of its magnetic field. Assume it’s radius is negligible.

A particle of mass m and charge q > 0 is at the origin at t = 0 and moving upward with velocity V~ = V yˆ.
Its subsequent trajectory is shown in the sketch. The magnitude of the velocity V =
V~
is always the same,

although the direction of V~ changes in time.



(a) (1 point) For y > 0, this positive charge is moving in a constant magnetic field which is either into the
page or out of the page. Is that magnetic field for y > 0 into or out of the page?
(b) (3 points) Derive an expression for the magnitude of the magnetic field for y > 0 in terms of q, m, R
and V .
(c) (3 points) For y < 0, the charge is moving in a different constant magnetic field. Is that field for y < 0
into or out of the page? What is the magnitude of that magnetic field in terms of q, m, R and V ?
(d) (3 points) How long does it take the charge to move from the origin to point P (see sketch) along the
x-axis. Give your answer in terms of R and V

Two singly ionized atoms move out of a slit at point S, as shown in figure, and into a magnetic
field of magnitude 0.100 T pointing into the page. Each has a speed of 1.00 × 106 m s−1

. The nucleus of the
first atom contains one proton and has a mass of 1.67 × 10−27 kg, whereas the nucleus of the second atom
contains a proton and a neutron and has a mass of 3.34 × 10−27 kg. Find their distance of separation when
they strike a photographic plate at P.

can you tell me how to solve these questions which are in chapter 16 of the book called Electricity and Magnetism by Munir H. Nayfeh and Morton K. Brussel?
1. Two perfectly conducting plates are located at y=0 and y=a. Consider a TM wave propagating between the plates with Hx=H0cos(kycosβ)cos(kzsinβ-ωt), and Hy=Hz=0 where β, , and k are constants.
(a) Determine an expression for E between the plates.
(b) Determine the relation between β, a, and k.
(c) Show that the time average of the Poynting vector is entirely in the z direction.
(d) Calculate the average power crossing the rectangle bounded by x=0, x=a, y=0, and y=b.
2.Consider the propagation of TM waves between two perfectly parallel conducting plates at y=0 and y=a.
(a) Determine the E and B fields propagating in the y-z plane between the plates.
(b) What is the lowest mode?
(c) Sketch the field patterns of the lowest mode.

Two singly ionized atoms move out of a slit at point S, as shown in figure, and into a magnetic
field of magnitude 0.100 T pointing into the page. Each has a speed of 1.00 × 106 m s−1
. The nucleus of the
first atom contains one proton and has a mass of 1.67 × 10−27 kg, whereas the nucleus of the second atom
contains a proton and a neutron and has a mass of 3.34 × 10−27 kg. Find their distance of separation when
they strike a photographic plate at P.

A particle of mass m and charge q > 0 is at the origin at t = 0 and moving upward with velocity V~ = V yˆ.
Its subsequent trajectory is shown in the sketch. The magnitude of the velocity V =



Mod V~


 is always the same,
although the direction of V~ changes in time.

(a) For y > 0, this positive charge is moving in a constant magnetic field which is either into the
page or out of the page. Is that magnetic field for y > 0 into or out of the page?
(b)Derive an expression for the magnitude of the magnetic field for y > 0 in terms of q, m, R
and V .
(c)For y < 0, the charge is moving in a different constant magnetic field. Is that field for y < 0
into or out of the page? What is the magnitude of that magnetic field in terms of q, m, R and V ?
(d) How long does it take the charge to move from the origin to point P (see sketch) along the
x-axis. Give your answer in terms of R and V .

A magnetic field does not exert a force on a what?

Two coils, held in fixed positions, have a mutual inductance of 100 μH. What is the peak voltage in one when a sinusoidal current given by I (t) = (10.0 A) sin
(1 000t) is in the other coil?

What is the resistance of a toaster that draws a current of 12A when connected to a 120V circuit?

Calculate the electric field inside the charge sphear
of charge density s = 8 x 4