Physics 122 Midterm - 14 Feb. 1997
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,
1 eV = $1.602 \times 10^{-19}$ J, and for electrons $q/m = 1.7588 \times 10^{11}$ C/kg and $m = 9.11 \times 10^{-31}$ kg.

1.

In his famous experiment demonstrating that the atom had a massive nucleus Rutherford (and his students Geiger and Marsden) used a beam of which was scattered from a gold foil.

2.

We connect in series a 12 V battery, a 100 ohm resistor and a capacitor, $C = 4.0 \times 10^{-5}$ Farads. At the instant we close the switch to complete the circuit the charge on the capacitor is $2.4 \times 10^{-4}$ Coulombs.

a)

What is the maximum charge on C after a very long time?

b)

Make a rough, qualitative drawing of Q vs. t to show how Q varies with time from Q₀ to $Q_{\rm max}$.

c)

How long does it take, in seconds, for the charge on C to increase from Q₀ to $3.6 \times 10^{-4}$ Coulombs?

3.

In the earth's Van Allen belt we observe electrons whose velocity parallel to the earth's magnetic field ( $B=0.11 \times 10^{-4}$ T in the Van Allen belt) is $5.1 \times 10^6$ m/s. The electrons have the same velocity perpendicular to B. Find:

a)

the energy of the electrons in eV.

b)

the radius of the circle (perpendicular to B).

c)

the time the electrons take to complete one circle.

4.

A battery ( $\varepsilon$=12 V) is connected to 9 equal resistors (R=300 ohms) as shown. How much current flows out of the battery?

5.

We have three long parallel wires all lying in a plane separated, as shown, by d=0.5 m. The currents flowing in the wire are: I₁=1.0 A, I₂=2.0 A, I₃=3.0 amps, in the directions indicated. What is the magnitude and direction of the magnetic force, per unit length, on wire 1?