Problems and Short Answer Questions

Write your answer to each of the following on the line provided on the answer sheet.

1. The figure shows two charges, Q₁ and Q₂. Assume Q₁ = +5.00 µC, Q₂ = +6.50 µC, r₁ = 7.00 cm and r₂ = 3.00 cm.

(a) Calculate the magnitude of the electrostatic force acting on Q₂.

(b) Is this force attractive or repulsive?

(c) Find the y-component of the electric field E at the origin.

2. A positron (q = +1.60x10^-19 C, m = 9.11x10^-31 kg) is projected out along the +x-axis with an initial speed of 351 m/s. It travels 0.550 cm and stops due to a uniform electric field in the region.

(a) Find the magnitude of the constant deceleration experienced by the positron.

(b) What is the magnitude of the electric field?

(c) What is the direction of the electric field vector (+i, -i, +j, -j, +k, -k)?

(d) How many positrons would have to be ejected from a source to total a charge of 1.50 nC?

3. An electric dipole, consisting of charges of magnitude 85.3 µC separated by 6.85 mm, is in an uniform electric field of magnitude 775 N/C. The dipole moment vector makes an angle of 23.0^o with the direction of the electric field.

(a) Calculate the magnitude of the torque acting on the dipole.

(b) Calculate the potential energy of the dipole.

4. A non-conducting sphere of radius R = 25.0 cm centered at the origin carries a charge Q = 3.60 µC that is uniformly distributed throughout the volume of the sphere.

(a) Find the flux of E through a spherical surface centered at the origin having a radius of 75.0 cm.

(b) Find the flux of E through a spherical surface centered at the origin having a radius of 15.0 cm.

(c) Determine the flux of E through one side of a cube which completely encloses the spherical charge distribution.

(d) Find the magnitude of E at a point 25.0 cm from the origin.

5. Two point charges are located as follows: +1.0 µC at (0.0,2.0) m and +4.0 µC at (2.0,-2.0) m.

(a) Calculate the electric potential at the origin due to these charges. Assume the conventional zero of potential.

(b) Calculate the potential energy of this charge distribution. Assume each of the charges was initially at infinity.

6. The diagram shows an isolated solid conducting sphere of radius 2.00 m. Point A has an electric potential of +4050 V. (Assume the conventional zero of potential)

(a) Determine the excess charge (magnitude and sign) on the surface of the sphere.

(b) Find the electric potential at the surface of the sphere (point B).

(c) Find the magnitude of the electrical potential difference between point A and a point infinitely remote from the sphere.

(d) Find the work needed to move a +5.00 µC charge from point B to point A.

7. An electric potential produced by some distribution of charge in a region is given by the formula

V = 2xy - 3zx + 5y²

with V in volts and the coordinates in meters. Determine the y-component of E at the point (2.0,2.0,2.0) m.

1. (a) 50.4 N   (b) repulsive   (c) -6.49x10⁷ N/C

2. (a) 1.12x10⁷ m/s²   (b) 6.38x10^-5 N/C   (c) -i   (d) 9.38x10⁹

3. (a) 1.77x10^-4 N m   (b) -4.17x10^-4 J

4. (a) 4.07x10⁵ N m²/C   (b) 8.79x10⁴ N m²/C   (c) 6.78x10⁴ N m²/C   (d) 5.18x10⁵ N/C

5. (a) 1.7x10⁴ V   (b) 8.0x10^-3 J

6. (a) +2.70x10^-6 C   (b) 1.22x10⁴ V   (c) 4050 V   (d) -4.05x10^-2 J

7. -24 N/C