Phys 3P36 - Computer Assignment 3
In example 5.10 Griths discusses the magnetic eld of a toroidal coil. In
this assignment you will model a toroid as a set of 1000 circular loops each
of radius R = 1. Let the inner and outer radii of the donut be 9R and
1
Vectors
V d3 r = S V da divergence theorem
V
V da = P V dl
Stokes theorem
S
A (B C) = B(A C) C(A B)
A (B C) = B (C A) = C (A B)
(f A) = f A + f A
(f A) = f A + f A
(A B) = B ( A) A ( B)
(A B) = A ( B) + B ( A) + (B )A + (A )B
(A B) = (B )A (A )B + A
Phys 3P36 - Homework 3 - Magnetic Forces
1. A point charge for which Q = 2 1016 C and m = 5 1026 kg is
moving in the combined elds:
E = 100 200 + 300V/m
x
y
z
B = 3 + 2 z T
x
y
If the charge velocity at t = 0 is (0) = (2 3 4) 105 m/s
v
x
y
z
determine th
Phys 3P36 - Homework 10
1. (a) By using the formula F = q B express Tesla in terms of
v
N,C,s,m.
(b) Show that the units of magnetic moment Am2 are the same as
J/T or Joule per Tesla.
2. In our derivation of the magnetic eld produced by a magnetized objec
Phys 3P36 - Homework 1- Current
1. Let J =
25
20
s + s2 +.01 z .
s
(a) Find the total current crossing the plane z = 0.2 in the z direction.
(b) Calculate the time derivative of the charge density
current density.
t
for this
(c) Find the outward current c
Phys 3P36 - Homework 5 - Amperes Law
1. Consider an innitely long cylinder of uniform charge density and
radius R. It is rotating around the axis of symmetry of the cylinder
with constant angular frequency .
(a) Determine J
(b) Determine the direction of
Phys 3P36 - Homework 19
1. Determine the vector potential A inside and outside a solenoid. Use
the symmetery between B = o J and A = B
2. Determine the self inductance of a solenoid using the A that you cal1
Jd
culated above and U = 2
A
1
Phys 3P36 - Hom
Phys 3P36 - Homework 15
1. A coil comprises 50 turns of wire wrapped around a square frame with
each side measuring 20 cm. If the coil is centered at the origin on the
plane z = 0 such that its sides are parallel to the x and yaxes and
is subject to B = 2
Phys 3P36 - Homework 12
1. Consider a disk of radius R and thickness t of constant magnetization
M = M z . Find
(a) B and H far outside the disk.
(b) What is producing H?
2. What is the dierence between a soft and a hard ferromagnetic in
terms of coercivi
Phys 3P36 - Computer Assignment 1
Consider the magnetic eld produced by a circular loop of radius R carrying
current I.
1. Letting the origin be at the center of, and z to the loop, write a
B
B
B
*.c program to calculate osI , o and ozI . Because of the c
Phys 3P36 - Homework 17
1. A square loop of side a recedes with a uniform velocity = u from an
v
s
innitely long lament carrying current I along z . One side of the loop
is parallel to z , the other is parallel to s. Show that the emf induced
in the loop
Phys 3P36 - Homework 8
1. Consider a uniformly charged insulating sphere of radius R that carries
a total charge Q and is set spinning with angular velocity about the
z axis.
(a) Calculate the magnetic dipole moment of the sphere.
(b) Find the approximate