1) A+4.51-nC charge is located 4.10 m from a-2.86-nC charge. Find the magnitude of the electrostatic force exerted by one charge on the other.
2) An alpha particle (charge = +2e) is sent at high speed toward a gold nucleus (charge = +79e). What is the electrical force acting on the alpha particle when it is2.227E-14 m from the gold nucleus?
3) An airplane is flying through a thundercloud at a height of 2.08E3 m. (This is a very dangerous thing to do because of updrafts, turbulence, and the possibility of electric discharge.) If there are charge concentrations of +40.0 C at height 3000 m within the cloud and -40.0 C at height 1000 m, what is the electric field E at the aircraft? Use a plus sign for a field pointing upward, and use a minus sign for a field pointing downward.
4) A small 2.00-g plastic ball is suspended by a 20.0-cm-long string in a uniform electric field. If the ball is in equilibrium when the string makes an angle θ=10.4 ° with the vertical as indicated, what is the net charge on the ball? For your calculation, you should use g=9.80 m/s2.
5) Suppose that we are able to travel past the Earth in a straight line. We travel a distance 4.01×107 m at a speed of 0.9007 c.
(a)
How long would this take as measured by someone standing on the Earth?(b)
How long would this take as measured by us in our moving reference frame?6)Suppose that we are able to cause a meter stick to move with a speed of 0.9007 c. What would be its length in our frame of reference?
7)A pion is an unstable particle which decays into a muon (which is also unstable and further decays into an electron). The pion's average lifetime when it is at rest is 26 ns. A particular pion moves with a speed of 0.9725 c.
(a)
What is its average lifetime as measured by an observer on Earth?
b)
What is the average distance it travels before decaying as measured by an observer on Earth?
(c)
What average distance would it travel if time dilation did not occur?
8)If astronauts could travel at v=0.968 c, we on Earth would say it takes about four years to reach Alpha Centauri, 4.37 light-years away. The astronauts disagree. (Caution: Do not use four years as the time interval measured on Earth. That is only approximate.)
(a)
How much time passes on the astronauts' clocks?
b)
What is the distance to Alpha Centauri as measured by the astronauts?
9)Suppose we are on our way to Alpha Centauri, which is 4.370 light-years away (in the reference frame of the earth). We are in a space ship which is traveling with a speed of 0.99657 c. When we are half-way there, we send a signal to both the earth and Alpha Centauri. The signals travel at the speed of light c. In the reference frame of the earth and Alpha Centauri, both signals travel 2.185 ly and thus arrive at their destinations at the same time.
(a)
In our reference frame, how long does it take for the signal to reach earth? Remember that in our reference frame, the distance between earth and Alpha Centauri is less than 4.370 ly because of length contraction.
(b)
In our reference frame, how long does it take for the signal to reach Alpha Centauri?
c)
These two events (the signal reaching earth and the signal reaching Alpha Centauri) are simultaneous in the earth's reference frame. How much time elapses between these two events in our reference frame?
10)Two charges, q1 and q2, are separated by 35.2 cm. If q1=20.4 nC, find the electric field at a point midway between the two charges for (a) q2=64.9 nC and for (b) q2=-64.9 nC. Use a positive sign if the field is pointing toward q2 and a negative sign if the field is pointing toward q1.
(a)
q2=64.9 nC
(b)
q2=-64.9 nC