Problem 11
In an experiment in space, one proton is held fixed and another proton is released from rest a distance of 2.50 mm away. (a) What is the initial acceleration of the proton after it is released? (b) Sketch qualitative (no numbers!) acceleration-time and velocity-time graphs of the released proton's motion.
Problem 12
A negative charge of \(-0.550 \space \mu\)C exerts an upward 0.600-N force on an unknown charge that is located 0.300 m directly below the first charge. What are (a) the value of the unknown charge (magnitude and sign); (b) the magnitude and direction of the force that the unknown charge exerts on the \(-\)0.550-\(\mu\)C charge?
Problem 13
Three point charges are arranged on a line. Charge \(q_3 = +\)5.00 nC and is at the origin. Charge \(q_2 = -\)3.00 nC and is at \(x = +\)4.00 cm. Charge \(q_1\) is at \(x = +\)2.00 cm. What is \(q_1\) (magnitude and sign) if the net force on \(q_3\) is zero?
Problem 17
Three point charges are arranged along the \(x\)-axis. Charge \(q_1 = +3.00 \space \mu\)C is at the origin, and charge \(q_2 = -5.00 \space \mu\)C is at \(x =\) 0.200 m. Charge \(q_3 = -8.00 \space \mu\)C. Where is \(q_3\) located if the net force on \(q_1\) is 7.00 N in the \(-\) \(x\)-direction ?
Problem 19
Two point charges are located on the \(y\)-axis as follows: charge \(q_1 = -1.50 \)nC at \(y = -\)0.600 m, and charge \(q_2 = +\)3.20 nC at the origin \((y = 0)\). What is the total force (magnitude and direction) exerted by these two charges on a third charge \(q_3 = +\)5.00 nC located at \(y = -\)0.400 m ?
Problem 20
Two point charges are placed on the \(x\)-axis as follows: Charge \(q_1 = +\)4.00 nC is located at \(x =\) 0.200 m, and charge \(q_2 = +\)5.00 nC is at \(x = -\)0.300 m . What are the magnitude and direction of the total force exerted by these two charges on a negative point charge \(q_3 = -\)6.00 nC that is placed at the origin?
Problem 23
A proton is placed in a uniform electric field of 2.75 \(\times 10^3 \space N/C\). Calculate (a) the magnitude of the electric force felt by the proton; (b) the proton's acceleration; (c) the proton's speed after 1.00 \(\mu\)s in the field, assuming it starts from rest.
Problem 25
A proton is traveling horizontally to the right at 4.50 \(\times 10^6\) m\(/\)s. (a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of 3.20 cm. (b) How much time does it take the proton to stop after entering the field? (c) What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)?
Problem 26
An electron is released from rest in a uniform electric field. The electron accelerates vertically upward, traveling 4.50 m in the first 3.00 \(\mu\)s after it is released. (a) What are the magnitude and direction of the electric field? (b) Are we justified in ignoring the effects of gravity? Justify your answer quantitatively.
Problem 27
(a) What must the charge (sign and magnitude) of a 1.45-g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 650 N\(/\)C? (b) What is the magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight?
