Physics 122 Midterm - 16 Feb. 1996
Note: Some constants you may need are: $k = 8.99 \times 10^9$ N m²/C,
$\mu_\circ = 4\pi \times 10^{-7}$ H/m,    $q/m = 1.7588 \times 10^{11}$ C/kg, for electrons.

1)

What is the main element which will be left in our sun after it has burned up most of its hydrogen?

2)

(a)

You have a uniform electric field (E = 150,000 V/m) in a box of volume 2.0 m³. What is the total electric field energy, in Joules, contained in the field of the box?

(b)

In the same box (volume 2.0 m³) you place, instead, a uniform magnetic field (B = 1.0 T). What is the total magnetic field energy, in Joules, contained in the field of the box?

3)

You have a circular coil (radius 0.5 m and containing 1,500 turns) which rotates (at an angular speed of 30 radians/sec) about an axis through the plane of the coil and through its centre.

(a)

What is the maximum EMF induced in the coil if its axis is perpendicular to a magnetic field of 0.2 T?

(b)

What is the average induced EMF?

4)

You have two long, concentric, coaxial, cylindrical conducting shells, one of radius R = 0.2 m and the other of radius 2R. You put a metal conducting cap at the far end, connecting the two cylinders and connect them to a 12 V battery.
 
You find that a current of 2.5 A flows out from the battery uniformly on the outer cylinder and into the battery uniformly on the inner cylinder. What is the magnetic field strength at r = 1.5 R?

5)

In Vancouver you have an electron gun which has accelerated electrons, from rest, through a voltage of 12 V. You aim the electrons horizontally north in the earth's magnetic field ( $0.2 \times 10^{-4}$ T) which points northward and down, at an angle of $30^\circ$ to the horizontal. What is the radius of the circle made by the electrons in their helical path?