Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

ELEC210: Problem set 3 (Lectures 4-7)

1.   Find the line charge density for a long conducting wire if the flux density 10 cm from the wire is D = 26.6 pC m-2.  Assume that the surrounding material has relative dielectric constant εr  = 1.

2.   An electric field in vacuum has the spatial dependence given below:

E =  xy2 − x z2 + xyz ̂(z)  V m"1

a)  Determine the divergence of the field at the point (1, 2, 3).

b)  Determine the charge density at that point.

3.   A parallel plate capacitor with spacing d has a charge Q. Find the change in energy stored if the plate spacing d is (a) halved (b) doubled.

Assume that the surrounding material has relative dielectric constant εr  =1.

4.   Consider a 100 m long copper wire with diameter of 1 mm. The electrical properties of copper include conductivity of 5.7x107  Sm- 1, electron mobility of 4x10-3  m2  V- 1  s- 1, and charge density of 1.4x1010  C m-3.

If 10 V is placed between the ends of the wire …

a)  Determine the current in the wire.

b)  Determine the electric field in the wire.

c)  Determine the average electron velocity in the wire.

5.    A long straight wire carries a current I = 10 A. At what distance from the wire does the magnetic field H have the value 1 A m- 1?

6.   A 5 turn loop with 0.5 m2  area situated in air has a uniform magnetic field normal to the plane of the loop.

a)   If the magnetic flux density changes at a rate of 8 mT s- 1, what is the emf at the terminals of the loop?

b)  If the emf at the loop terminals is 150 mV, what is the rate of change of the magnetic flux density?

7.   Four straight conductors form a square with a magnetic field B perpendicular to the square. If all conductors move outwards with the same velocity v while remaining in contact with each other at the corners, find V(rms) induced in the square loop when its area is 2 m2, v = 4 m/s    and B = cos(2π f t) where f = 2 kHz.

8.   The magnetic field around a current carrying conductor at a given point is given by:

H =  3 − 7y + 2x̂(z)  A m- 1

Find the current density J in the conductor.