Chipola Junior College - Spring 2000

PHY 1054 - Electric Force Field Practice

1. Consider the distribution of point charges shown below. The coordinate axes are marked in centimeters.

a) Find the electric field at the origin for this distribution of charges.

b) Calculate the electric field on the y-axis at y=7 cm.

c) Find the force on an additional charge of qo=4.5x10-9 C if it is placed at the origin.

2. Assume a commercial airplane with a mass of 5000 kg flies by electrical repulsion with the ground. The bottom of the plane can be charged up to any value as the plane is in operation. Also assume the ground is charged at 1000 C. In this problem, include the effect of gravity W=-mg (FBDs may be useful).

  1. How much charge must be put on the plane in order for it to accelerate upward at 5 m/s2? Assume the bottom of the plane is separated from the ground by a meter and a half.
  2. How much charge must be put on the plane in order for it to decelerate 5 m/s2 if it is 500 m above the ground?
  3. Calculate the charge needed for the plane to hover above the ground (a=0) at 1000 m.
  4. Calculate the electric field directly between the plane and ground when it is 500 m above the ground.

3. Consider the distribution of point charges shown below. The coordinate axes are marked in centimeters.

a) Find the electric field at the origin for this distribution of charges.

b) Calculate the electric field on the y-axis at y=4 cm.

c) Find the force on an additional charge of qo=5x10-8 C if it is placed at the origin.

4. Consider the Bohr model of the hydrogen atom: a proton (charge qp=1.6x10-19 C) lies stationary in the middle of the atom and a single electron orbits in a circle around the proton. The Bohr model predicts that the electron can only occupy set orbits with specific radii. The radius of the first orbit is r1=0.53x10-10 m and the second orbit is r2=2.12x10-10 m.

a) Calculate the electric field due the proton at the position of the first Bohr radius r1.

b) Calculate the electric field due the proton at the position of the second Bohr radius r2.

c) Calculate the force on an electron placed at the position of the first Bohr radius.

5. A charge of 3x10-8 C is placed at the origin and a second charge of 7x10-8 C is placed at a point 5 cm to the right of the origin.

a) Calculate the electric field at a point 10 cm to the left of the origin.

b) If a point charge of 9x10-9 C is placed 10 cm to the right of the origin then what is the force on this last charge (due to the first two charges)?

c) Now calculate the electric field at a point 10 cm to the left of the origin due to all three charges.

d) What is the electric field 5 cm above the origin (on the y-axis)?

6. A 0.25 kg coke can is charged up to 1.5x10-4 C and set on a table.

  1. In an effort to get the can without getting up, you stretch out your hand to within 1.5 meters of the can and find that nothing happens. Remembering from physics class that you need a negative charge on your hand to attract the can, you rub a silk handkerchief on your hand until you get a charge of -2.7x10-3 C (on your hand). Calculate the force between your hand and the coke can.
  2. Ignoring the weight of the can (it’s in the y-direction, anyway), how close must your hand get to the can in order to achieve an acceleration of 0.5 m/s2? Newton’s 2nd law: F=ma!
  3. Now calculate the electric field at a point halfway between the can and your hand for the situation described in part (a).
  4. If a balloon charged to 7x10-6 C floats to the point halfway between the can and hand (as described in (a) and (c)), then find the force on the balloon, both magnitude and direction.