212 - Problem Set 2

Physics 212 Spring 2009 Problem Set #2

1)A charge of +3.5 µC is placed on the x axis at x = +0.55 m,

while a charge of –15 µC is placed at the origin. (a) Calculate the magnitude and direction of the net electric field on the x axis at x = +0.8 m. (b) Determine the magnitude and direction of the force that would act on a charge of –8.0 µC if it was placed on the x axis at x = +0.8 m.

2)A small sphere of mass 12 g carries a charge of –18 µC. Determine the magnitude and direction of an electric field that would be needed to cause the sphere to float in the air. 3) A proton accelerates from rest in a uniform electric field of magnitude 640 N/C. At a later time, its speed is 1.20 x 10 6 m/s. (a) Calculate the acceleration of the proton. (b) How much time is needed for the proton to reach this speed? (c) How far has the proton traveled during this time? (d) What is the proton’s kinetic energy at this time?

3) a) 6.11 x 1010 m/s2 b) 1.96 x 10-5 s c) 11.8 m d) 1.2 x 10-15 J 4) 756 N/C, 70.1° 5) 5.25 x 10-6 C

8) (a) 1.52 x 105 m/s (b) 6.49 x 106 m/s 9) 8.09 x 10-7 J 10) (b) 2 x 10-14 N

6) Points A and B have potentials of +250 V and –150 V respectively. An alpha particle (a helium nucleus that contains two protons and two neutrons) starts from rest at A and accelerates toward B. When the alpha particle arrives at B, what kinetic energy (in electron volts) does it have?

7)Three point charges are located as shown.

(a) Determine the electric potential at point A due to these charges. (b) What is the electric potential energy of a +3.5 µC charge placed at A?

4) Positive charges are placed at the three corners of a rectangle as shown. Calculate the magnitude and direction of the electric field at the fourth corner.

-20 µC

6 nC 4 cm 20 cm

3 nC

5 nC

A

3.6 µC

60 cm

5) A 2 g plastic sphere is suspended by a 20 cm long piece of string. The sphere is hanging in a uniform electric field of magnitude 1000 N/C. See diagram. If the sphere is in equilibrium when the string makes a 15° angle with the vertical, what is the net charge on the sphere?

2 cm

6 µC

3 cm

8) Calculate the speed of (a) a proton and (b) an electron after they have been accelerated from rest through a potential difference of 120V. 9)

15°

ANSWERS: 1) a) 2.9 x 105 N/C, +x direction 6) 8.0 x 102 eV b) 2.3 N, - x direction 7) (a) –1.1 x 106 V 2) 6.5 x 103 N/C, down (b) –3.8 J

A charge of 9 nC is located at the origin. How much work is required to bring a positive charge of 3 nC from infinity to a location that is 30 cm away from the origin?

10) An electron is placed between the plates of a charged capacitor as shown. The plates have a potential difference of 2500 V. a) In which direction will the electron feel a force? b) What is the magnitude of the force that the electron will feel? c) Is the left plate negatively charged or positively charged?

2 cm