Homework #11
Problem 1.
[35%] Using the Amperes law, find the magnetic field at distance s from the center
of a circular toroid (in the plane of the toroid at z=0). Consider all three possible
cases: (i) s < R-r, (ii) R-r < s < R+r, (iii) s > R+r (see fig
Homework #8
Problem 1.
(a) [25%] Find the potential in the infinite slot of Example 3.3 (see page 127) if the
boundary at x = 0 consists of two metal strips: one, from y = 0 to y = a/2, is held at
a constant potential V0, and the other, from y = a/2 to y
Homework #6
Problem 1.
(a) [15%] Find the energy of a uniformly charged conducting spherical shell (empty
inside) of radius R and charge q by making use of Eq. (2.45). [Hint: You need to
obtain the result for the electric field with the help of the Gausss
Homework #3
Problem 1 (25%)
A thin bar of length L = 10 cm carries a uniform linear charge density l = 3 C/m. Find
the magnitude (measured in the SI units) and direction of the Coulomb force on a test
y
charge Q = 2 C at a distance a = 6 cm away from one
Homework #10
Problem 1.
(a) [10%] A particle with charge q=40 C moves eastward with speed v=2 km/s. The
magnetic field of the earth is about 510-5 T directed north. Find the (magnitude and
direction of) magnetic force on the particle.
(b) [10%] What is th
Homework #1
Problem 1 (15%)
Calculate the scalar (dot) product, the cross product, and the angle between the
following two vectors:
= 3 + 2
and
= 2 +
z
Problem 2 (10%)
Find the angle between two adjacent face diagonals of a cube (see
the figure) using
Homework #9
Problem 1.
(a) [30%] A hydrogen atom (with the radius of a = 5.2910-11 m) is situated between
two metal plates 0.5 cm apart, which are connected to opposite terminals of a 12 V
battery. What fraction of the atomic radius does the separation di
Homework #2
Problem 1 (20%)
Find the divergence of the following vector field using spherical coordinates:
= 2 sin + 2 cos + 2 ( )2
Problem 2 (20%)
Find the curl of the following vector field using cylindrical coordinates:
= 2 sin + 2 .
Problem 3 (20%)
Homework #5
Problem 1.
(a) [20%] Find the electric potential at a point P, a distance z
above the center of a circular loop of radius r, which carries a
uniform line charge . [Use eq. (2.30) in the textbook.]
(b) [10%] Using the result for the electric po
Homework #4
Problem 1 (25%)
An infinite plane slab of thickness a carries a uniform volume charge density . Using
the Gausss law, find the electric field as a function of z (by assumption, the slab is
located between z=-a/2 and z=a/2). Plot schematically