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(Multiple choice)

**(1)**

A lithium nucleus and an α particle are at rest. The lithium nucleus has a charge of +3e and a mass of 7 u; the α particle has a charge of +2e and a mass of 4 u. Which of the methods below would accelerate them both to the same kinetic energy?

(a) Accelerate them through the same electrical potential difference.

(b) Accelerate the α particle through potential V1 and the lithium nucleus through V1.

(c) Accelerate the α particle through potential V1 and the lithium nucleus through V1.

(d) Accelerate the α particle through potential V1 and the lithium nucleus through (2 × 7)/(3 × 4)V.

(e) None of the above.

**(2)**

Two charged metal spheres are connected by a wire, and sphere A is larger than sphere B (Figure). The magnitude of the electric potential of sphere A is

(a) Greater than that at the surface of sphere B.

(b) Less than that at the surface of sphere B.

(c) The same as that at the surface of sphere B.

(d) Greater than or less than that at the surface of sphere B, depending on the radii of the spheres.

(e) Greater than or less than that at the surface of sphere B, depending on the charge on the spheres.

**(3)**

Two equal positive point charges +Q are on the x axis. One is at x = −a and the other is at x = +a. At the origin,

(a) E = 0 and V = 0.

(b) E = 0 and V = 2kQ/a.

(c) E = (2kQ^{2}/a^{2}) and V = 0.

(d) = (2kQ^{2}/a^{2}) and V = 2kQ/a.

(e) None of the above is correct.

**(4)**

The electrostatic potential is measured to be V(x, y, z) = 4|x| + V_{0}, where V_{0} is a constant. The charge distribution responsible for this potential is

(a) A uniformly charged thread in the xy plane.

(b) A point charge at the origin.

(c) A uniformly charged sheet in the yz plane.

(d) A uniformly charged sphere of radius 1/π at the origin.

**(5)**

Two point charges of equal magnitude but opposite sign are on the x axis; +Q is at x = −a and −Q is at x = +a. At the origin,

(a) E = 0 and V = 0.

(b) E = 0 and V = 2kQ/a.

(c) E = (2kQ^{2}/a^{2}) and V = 0.

(d) E = (2kQ^{2}/a^{2}) and V = 2kQ/a.

(e) None of the above is correct.

**(6) True or false:**

(a) If the electric field is zero in some region of space, the electric potential must also be zero in that region.

(b) If the electric potential is zero in some region of space, the electric field must also be zero in that region.

(c) If the electric potential is zero at a point, the electric field must also be zero at that point.

(d) Electric field lines always point toward regions of lower potential.

(e) The value of the electric potential can be chosen to be zero at any convenient point.

(f) In electrostatics, the surface of a conductor is an equipotential surface.

(g) Dielectric breakdown occurs in air when the potential is 3 × 10^{6} V.

**(7)**

(a) V is constant on a conductor surface. Does this mean that σ is constant?

(b) If E is constant on a conductor surface, does this mean that σ is constant? Does it mean that V is constant?

**(8)**

An electric dipole has a positive charge of 4.8 × 10^{−19} C separated from a negative charge of the same magnitude by 6.4 × 10^{−10} m. What is the electric potential at a point 9.2 × 10^{−10} m from each of the two charges?

(a) 9.4 V

(b) Zero

(c) 4.2 V

(d) 5.1 × 10^{9}V

(e) 1.7 V

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