Potential energy of point-charges: Consider the group of three+2.4 nC point charges shown in the figure. What is the electric potential energy of this system of charges relative to infinity? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Radiation pressure: A radiometer has two square vanes (1.0 cm by 1.0 cm), attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is 6.0 cm from the axis. One vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electromagnetic wave with an intensity of 0.30 kW/m2 is incident normally upon the vanes. What is the radiation pressure on the blackened vane? (c = 3.00 × 108 m/s, μ0 = 4π × 10-7 T ∙ m/A, ε0 = 8.85 × 10-12 C2/N ∙ m2)

In proton-beam therapy, a high-energy beam of protons is fired at a tumor.  As  the protons stop in the tumor, their kinetic energy breaks apart the tumor’s DNA, thus killing the tumor cells. For one patient, it is desired to deposit 0.09 J of proton energy in the tumor. To create the proton beam, protons are accelerated from rest through a 9.0×103 kV potential difference. What is the total charge of the protons that must be fired at the tumor? 

The electric field strength is 5.00×104  N/C inside a parallel-plate capacitor with a 1.60 mm  spacing. A proton is released from rest at the positive plate. What is the proton’s speed when it reaches the negative plate? (mass of proton = 1.67 x 10-27 kg, charge of an proton = 1.60 x 10-19 C)

Cylindrical capacitors: The capacitance per unit length of a very long coaxial cable, made of two concentric cylinders, is 50 pF/m. What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Current: In a certain electroplating process gold is deposited by using a current of 14.0 A for 19 minutes. A gold ion, Au+, has a mass of approximately 3.3 × 10-22 g. How many grams of gold are deposited by this process?

The electric field strength is 4.60×104  N/C inside a parallel-plate capacitor with a 2.20 mm  spacing. A proton is released from rest at the positive plate. What is the proton’s speed when it reaches the negative plate? (mass of proton = 1.67 x 10-27 kg, charge of an proton = 1.60 x 10-19 C)

In the figure shown below, q = -2.3 nC. What is the electric potential at the point indicated with the black dot? Make sure to include units. 

Radiation pressure: The total electromagnetic power emitted by the sun is 3.8 × 1026 W. What is the radiation pressure on a totally absorbing satellite at the orbit of Mercury, which has an orbital radius of 5.8 × 1010 m? (c = 3.00 × 108 m/s, μ0 = 4π × 10-7 T ∙ m/A, ε0 = 8.85 × 10-12 C2/N ∙ m2)

Energy in capacitors: A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?