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1. Use Coulomb’s Law to find the following
properties of the net electric field at A due to the two negative charges. (Q
= - 6.0µC) The triangle is isosceles,
i.e. the two inclined sides are equal.
k = 9.0x10 9 Nm2/C2.
(a) (18 points) The magnitude Enet of
the net electric field .
(b) (18 points) The direction of the net electric field.
(c) (8 points) What is the potential at point A due
to the two negative charges. (Hint: Add the potentials due to each
charge.)
(d) Extra Credit (22 points) Repeat parts (a), (b) and (c) for the following diagram
in which the left charge is + 6.0µC
and the right charge is - 6.0µC.
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2.(44 points) In the figure below a
proton is fired rightward, horizontally with an initial speed of exactly 200,000 m/s from the
midpoint of the capacitor toward the
vertical positive plate. The parallel negative plate on the left is defined
to be at potential V-
= 0 (V) and the right positive plate at potential V+ = 500.00 (V). The distance between the inner surfaces of the plates is d
= 0.1000 m . The proton mass is mp =
1.67x10-27 kg
and charge magnitude is
e = 1.6x10-19 (C
). Ignore the force of gravity.
(a) (16 points) Prove, mathematically, that the
proton has insufficient speed to reach the right plate. In other words, show
that the proton will not reach the right plate. Show all work carefully in
making your arguments.
(b) (24 points) What is the proton’s speed just before it
collides with the negative plate? Compare your answer with the proton’s
initial speed and explain the difference.
(c) (4 points) Suppose the separation between the
plates was reduced by one half to a smaller distance d =
0.0500 m and the initial location and speed and voltages on the plates were the same.
Would your answer to (a) change, i.e. would the proton have
insufficient speed to reach the right
plate? Explain. Would your answer to (b) change? Explain.
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3. (32 points) A 12.0 (V) battery is
connected to a
resistor network as shown below in fig (i).
(a) (10 points) What’s the equivalent resistance Rp of the circuit in
in fig (ii)?
(b) (1) What’s the voltage difference across the 40.0 ohm resistor?
(c) What is current I in fig (ii)?
(d) (10) What’s the current I1 through the 40.0 ohm resistor?
(e) (1) What’s the voltage difference across the 30.0 ohm resistor?
(f) (10) What’s the current I2 through the 30.0 ohm resistor?
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