Problem 21.

Three small spheres are enclosed in surface carrying charges q1 = 4 nC, q2 = -10.00 nC, and q3 = 5 nC.

 Surface (s)                        What it encloses

s1                                        q1

s2                                        q2

s3                                        q1 and q2

s4                                        q1 and q3

s5                                        q1, q2 and q3

Find the net electric flux through each of the following closed surfaces.

(a) s1

(b) s2    

(c) s3        

(d) s4

(e) s5

Solution

Problem 22.

Two plastic spheres, each carrying charge uniformly distributed throughout its interior, are initially placed in contact and then released. The first sphere has a diameter of 60 cm, a mass of  50 g, and contains   of charge. The second sphere has a diameter of 40 cm, a mass of  150 g and contains    of charge. Assume that no other forces are acting on them.

(a) Find the maximum speed achieved by the first sphere.

(b) Find the maximum acceleration achieved by the first sphere.

Solution

Problem 23.

A particle with a charge of +8 nC is in a uniform electric field E directed to the left. It is released from rest and moves to the left. After it has moved 3 cm, its kinetic energy is found to be

(a) What work was done by the electric force?

(b) What is the potential of the starting point with respect to the endpoint?

(c) What is the magnitude of E?

Solution

Problem 24.

A total electric charge of 8 nC is distributed uniformly over the surface of a metal sphere with a radius of 27 cm. If the potential is zero at a point at infinity, find the value of the potential at the following distances from the center of the sphere.

(a) 52 cm

(b) 20 cm

(c) 9 cm

Solution

Problem 25.

A potential difference of 10 kV is established between parallel plates in air.

(a) If the air becomes electrically conducting when the electric field exceeds , what is the minimum separation of the plates?

(b) When the separation has the minimum value calculated in part (a), what is the surface charge density on each plate?

Solution

Problem 26.

An alpha particle with kinetic energy 10 MeV makes a head-on collision with a lead nucleus at rest. What is the distance of closest approach of the two particles? (Assume that the lead nucleus remains stationary and that it may be treated as a point charge. The atomic number of lead is 82. The alpha particle is a helium nucleus, with atomic number 2.)

Solution

Problem 27.

In a certain region of space, the electric potential is is , , where A, B, and C are positive constants.

(a)  Calculate the x-, y-, and z-components of the electric field.

(b) At which points is the electric field equal to zero?

Solution

Problem 28.

A point charge is held stationary at the origin. A second point charge is moves from the point x = 0.20 m, y = 0 to the point x = 0.3 m, y = 0.35 m. How much work is done by the electric force on ?

Solution

Problem 29.

A parallel-plate air capacitor has a capacitance of 800 pF. The charge on each plate is 6 µC. What is the potential difference between the plates?

Solution

Problem 30.

A parallel-plate air capacitor of capacitance of 100 pF has a charge of magnitude 0.1 µC on each plate. The plates are 0.5 mm apart.

(a) What is the potential difference between the plates?

(b) What is the area of each plate?

(c) What is the electric-field magnitude between the plates?

(d) What is the surface charge density on each plate?

Solution

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