Problem 1
A point charge \(q_1 = +\)2.40 \(\mu\)C is held stationary at the origin. A second point charge \(q_2 = -\)4.30 \(\mu\)C moves from the point \(x =\) 0.150 m, \(y =\) 0 to the point \(x =\) 0.250 m, \(y =\) 0.250 m. How much work is done by the electric force on \(q_2\)?
Problem 2
A point charge \(q_1\) is held stationary at the origin. A second charge \(q_2\) is placed at point a, and the electric potential energy of the pair of charges is \(+5.4 \times 10^{-8} \)J. When the second charge is moved to point \(b\), the electric force on the charge does \(-1.9 \times 10^{-8}\) J of work. What is the electric potential energy of the pair of charges when the second charge is at point \(b\)?
Problem 4
(a) How much work would it take to push two protons very slowly from a separation of \(2.00 \times 10^{-10}\) m (a typical atomic distance) to \(3.00 \times 10^{-15}\) m (a typical nuclear distance)? (b) If the protons are both released from rest at the closer distance in part (a), how fast are they moving when they reach their original separation?
Problem 5
A small metal sphere, carrying a net charge of \(q_1 = -\)2.80 \(\mu\)C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of \(q_2 = -\)7.80 \(\mu\)C and mass 1.50 g, is projected toward \(q_1\). When the two spheres are 0.800 m apart, \(q_2\), is moving toward \(q_1\) with speed 22.0 m\(/\)s (\(\textbf{Fig. E23.5}\)). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. (a) What is the speed of \(q_2\) when the spheres are 0.400 m apart? (b) How close does \(q_2\) get to \(q_1\)?
Problem 7
Two protons, starting several meters apart, are aimed directly at each other with speeds of \(2.00 \times 10^5\) m\(/\)s, measured relative to the earth. Find the maximum electric force that these protons will exert on each other.
Problem 8
Three equal 1.20-\(\mu$$C\) point charges are placed at the corners of an equilateral triangle with sides 0.400 m long. What is the potential energy of the system? (Take as zero the potential energy of the three charges when they are infinitely far apart.)
Problem 10
Four electrons are located at the corners of a square 10.0 nm on a side, with an alpha particle at its midpoint. How much work is needed to move the alpha particle to the midpoint of one of the sides of the square?
Problem 11
Three point charges, which initially are infinitely far apart, are placed at the corners of an equilateral triangle with sides \(d\). Two of the point charges are identical and have charge \(q\). If zero net work is required to place the three charges at the corners of the triangle, what must the value of the third charge be?
Problem 12
An object with charge \(q = -6.00 \times 10^{-9}\) C is placed in a region of uniform electric field and is released from rest at point \(A\). After the charge has moved to point \(B\), 0.500 m to the right, it has kinetic energy \(3.00 \times 10^{-7}\) J. (a) If the electric potential at point \(A\) is \(+\)30.0 V, what is the electric potential at point \(B\)? (b) What are the magnitude and direction of the electric field?
Problem 13
A small particle has charge \(-5.00\) \(\mu\)C and mass \(2.00 \times 10^{-4}\) kg. It moves from point \(A\), where the electric potential is \(V_A = +\)200 V, to point \(B\), where the electric potential is \(V_B = +\)800 V. The electric force is the only force acting on the particle. The particle has speed 5.00 m\(/\)s at point \(A\). What is its speed at point \(B\)? Is it moving faster or slower at \(B\) than at \(A\)? Explain.
