PHYS 2212 Module 1 Self Assessment Practice Problems

1.1
A charge of 4.99 nC is placed at the origin of an xy-coordinate system, and a charge of -2.05 nC is placed on the positive x-axis at x = 4.05 cm. A third particle of charge 5.98 nC is now placed at the point x = 4.05 cm, y = 3.01 cm. Find the x- and y-components of the total force exerted on the third charge by the other two charges.
Answer: 8.43 x 10^-5 N and -5.94 x 10^-5 N (Click and drag over the invisible text to highlight and view the answers)

1.2
Consider a model of a hydrogen atom in which an electron is in a circular orbit of radius r = 5.89 x 10^-11 m around a stationary proton. What is the speed of the electron in its orbit?
Answer: 2.07 x 10⁶ m/s

1.3
A negative charge of -0.510 µC exerts an upward 0.700-N force on an unknown charge that is located 0.400 m directly below the first charge.
(a) What is the value of the unknown charge (magnitude and sign)?
(b) What is the magnitude of the force that the unknown charge exerts on the -0.510 µC charge?
(c) What is the direction of this force?
Answer: (a) +2.44 x 10^-5 C (b) 0.7 N (c) downward

1.4
Two point charges are placed on the x-axis as follows: charge q₁ = 4.02 nC is located at x = 0.197 m, and charge q₂ = 5.05 nC is at x = -0.303 m.
(a) What is the magnitude of the total force exerted by these two charges on a negative point charge q₃ = -5.98 nC that is placed at the origin?
(b) What is the direction of the total force exerted by these two charges on a negative point charge q₃ = -5.98 nC that is placed at the origin?
Answer: (a) 2.62 x 10^-6 N (b) +x direction

1.5
(a) How far does an electron (q = –e) have to be from a proton (q = +e) so that its acceleration is the same as that of a freely falling object at the earth’s surface?
(b) Suppose the earth were made only of protons but had the same size and mass it has presently. What would be the acceleration of an electron released at the surface?
Answer: (a) 5.1 m (b) 2.2 x 10⁴⁰ m/s²

1.6
Imagine two 3.0-gram bags of protons (q = +e), one at the earth’s north pole and the other at the south pole.
(a) How many protons are in each bag?
(b) Calculate the gravitational attraction that each bag exerts on the other.
(c) Calculate the electrical repulsion that each bag exerts on the other.
Answer: (a) 1.8 x 10²⁴ (b) 3.69 x 10^-30 N (c) 4.56 x 10⁶ N

1.7
A small 12.7 gram plastic ball is tied to a very light 29.6 cm string that is attached to the vertical wall of a room. A uniform horizontal electric field exists in this room as well. When the ball has been given an excess charge of -1.40 µC, you observe that it remains suspended, with the string making an angle of 17.4° with the wall. Find the magnitude and direction of the electric field in the room.
Answer: 2.79 x 10⁴ N/C to the left

1.7

A small 12.7 gram plastic ball is tied to a very light 29.6 cm string that is attached to the vertical wall of a room. A uniform horizontal electric field exists in this room as well. When the ball has been given an excess charge of -1.40 µC, you observe that it remains suspended, with the string making an angle of 17.4° with the wall. Find the magnitude and direction of the electric field in the room.

Answer: 2.79 x 10⁴ N/C to the left

1.8
Two tiny spheres of mass = 8.30 milligrams each carry charges of equal magnitude, 82.0 nC, but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m. When a horizontal uniform electric field that is directed to the left is turned on, the spheres hang at rest with the angle θ between the strings equal to 58.0°.
(a) Which ball (the one on the right or the one on the left) has positive charge?
(b) What is the magnitude of the electric field?
Answer: (a) the one on the left has positive charge (b) 3.34 x 10³ N/C

1.9
An electron is projected with an initial speed v₀ = 1.70 x 10⁶ m/s into the uniform field between the parallel plates in the figure. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.
Answer: 411 N/C

1.9

An electron is projected with an initial speed v₀ = 1.70 x 10⁶ m/s into the uniform field between the parallel plates in the figure. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.

Answer: 411 N/C

1.10
Point charges q₁ = -4.5 nC and q₂ = +4.5 nC are separated by 3.1 mm, forming an electric dipole.
(a) Find the electric dipole moment (magnitude and direction).
(b) The charges are in a uniform electric field whose direction makes an angle of 36.9° with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude 7.2 x 10^-9 N•m?
Answer: (a) 1.4 x 10^-11 C•m toward q₂ (b) 860 N/C