Physics 101 Quiz Solutions

Physics 101 Quiz Solutions

1. Two rectangular parallel metal plates are separated by a small distance. How many electrons must be transferred from one plate to the other to give each plate a charge of ±157 nC?

981 billion electrons must be transferred from one plate to the next to place 157 nC on charge on each plate.

1. A large metal sphere is given a negative charge. Two smaller metal spheres, labeled A and B, are mounted on insulating stands and are free to move. A flexible grounding wire is also available. See figure. Describe in a series of steps how you would

1. Give both spheres a negative charge.

Simply touch each small sphere to the larger sphere and some of the excess negative charges will transfer to each smaller sphere.

1. Give one sphere a positive charge and the other sphere a negative charge.

While the small spheres are far from the large negative sphere touch them together. /
Bring the two smaller spheres (still touching each other) close to the large negative sphere. The nearer sphere will be polarize positive and the farther sphere will be polarized negative. /
Separate the small spheres from each other while close to the large negative sphere. /
The polarization is now locked into each sphere. /

1. Give both spheres a positive charge

While the small spheres are far from the large negative sphere touch them together. /
Bring the two smaller spheres (still touching each other) close to the large negative sphere. The nearer sphere will be polarize positive and the farther sphere will be polarized negative. /
Ground the farther small sphere, allowing the negative charges to run to ground leaving the two smaller spheres with a positive charge. /
Disconnect the ground wire and separate the small spheres from each other while close to the large negative sphere. /
The polarization is now locked into each sphere. /

1. Two charges of -5nC and + 15nC are separated by a distance of 0.25 cm. What is the magnitude and direction of the electric force between them?

This is a straight forward Coulomb’s Law problem. Since the charges are of opposite polarity the force will be radialy attractive.

The force between the two charges is 0.1 Newtons.

A note is worthy here: Many times the electrical force between charges may not seem like a large number. Frequently the forces between charges will be very small especially when dealing with individual electrons, protons or ions. However, the masses of those particles are also typically very small – on the order of 10-25 to 10-31 kg. Thus even very small forces can cause large accelerations and high speeds in these circumstances.

1. A small sphere, charged to -7 nC, is suspended from a fine thread hanging at an angle of 30 degrees to the right in a uniform electric field of 50,000 N/C.
2. What is the direction of the electric field? Sketch it on the diagram.

E must be directed to the left since the force on the charge is directed towards and right AND the charge is a negative charge.

1. Sketch the free body diagram of forces on the small sphere.

1. Derive and calculate the mass of the sphere?

The net force on the sphere is zero. Balance the forces in the horizontal and vertical

Horizontally: T∙sin(30) = FElec

Vertically: T∙cos(30) = mg

Combining

The mass of the sphere is 61.9 milligrams

1. A light weight 2.5 g Styrofoam sphere carries a charge of 375 nC. It is placed between two horizontal parallel plates carrying equal and opposite charges sit on a lab bench and create a uniform electric field between them. The electric field between the plates is set so that the Styrofoam sphere will “float” between the plates.
2. What is the magnitude of the electric field required to “float” the Styrofoam sphere?

The sphere will “float” when the downward weight (mg) is balanced by an upward electric force (qE).

Therefore mg = qE, or

The electric field strength is 65,3333 N/C and directed upward.

1. Which of the parallel plates has a positive charge? The upper or lower? Explain your choice.

The lower plate must be positive while the upper plate is negative for the E field to be irected upwards.

1. An electric dipole is oriented along the y-axis as shown in the figure. The upper portion of the dipole is +Q and the lower portion is –Q. An electron is placed on the x-axis as shown.
2. What is direction of the NET electric field from the dipole at the electron’s position? Justify your answer with a sketch and explanation. No calculations are needed.

The electric field at the electron’s position is show due to each of the dipole charges (Positive charge radial away, negative charge radial toward). You can see from the symmetry of the problem that the horizontal components of each electric field must cancel and the vertical components must add. Thus the Net E field is directed downward, as shown.

1. In what direction will the electron initially accelerate if released from its position?

The force on the electron from a downward directed E field will be upward. The electron will initially accelerate upward.