### All AP Physics C: Mechanics Resources

## Example Questions

### Example Question #1 : Electricity

A hollow metal sphere with a diameter of 10cm has a net charge of distributed uniformly across its surface. What is the magnitude of the field a distance 2.0m from the center of the sphere?

**Possible Answers:**

**Correct answer:**

Relevant equations:

(electric field of point charge)

Anywhere outside the metal sphere, the electric field is the same as it would be for a point charge of the same magnitude, located at the center of the sphere. So, calculate the electric field of a point charge given:

Plugging in gives:

### Example Question #1 : Electricity And Magnetism Exam

Two infinite parallel conducting sheets each have positive charge density . What is the magnitude and direction of the electric field to the right of the right sheet?

**Possible Answers:**

, to the left

, to the right

, to the right

, to the right

**Correct answer:**

, to the right

Relevant equations:

(field due to single infinite plane)

Electric field is additive; in other words, the total electric field from the two planes is the sum of their individual fields:

The direction of the electric field is away from positive source charges. Thus, to the right of these positively charged planes, the field points away to the right.

### Example Question #1 : Electricity And Magnetism Exam

Four particles, each of charge , make up the four corners of a square with equal side lengths of . For the charge in the top left corner of the square, in what direction is the net force that it experiences due to its interactions with the other three particles?

**Possible Answers:**

downwards of right

upwards of left

Directly to the left

Directly to the right

**Correct answer:**

upwards of left

The correct answer is 45 degrees upwards of left. Since all particles have charge , all forces will be repulsive (there will be no attracting forces). The particle in the top-right corner creates a repulsive force directly to the left, and the particle in the bottom-left corner creates a repulsive force directly upwards. These are equal in magnitude, since they are both at distance from the top left corner. The bottom-right corner also creates a repulsive force, but acts along the same direction as the vector sum of a leftwards and upwards force.

### Example Question #1 : Electricity

Consider a spherical capacitor made of two nested spheres. The smaller sphere has a radius of and a charge of , and lies within a larger sphere with radius and a charge of .

Which of the following equations accurately describes the capacitance of this spherical capacitor?

**Possible Answers:**

Due to symmetry, this scenario would not produce capacitance

**Correct answer:**

To solve this problem, we will need to derive an equation.

We know that:

We can use Gauss's law to derive the electric field between the two circles yielding:

Doing our integration with respect to from to , we get:

We can plug this back into our equation for capacitance to get:

### Example Question #1 : Electricity And Magnetism Exam

We have a point charge of . Determine the electric field at a distance of away from that charge.

**Possible Answers:**

**Correct answer:**

Coulomb's law for the electric field from point charges is , where we know the values of the following variables.

Using these values, we can solve for the electric field.

### Example Question #1 : Electricity And Magnetism Exam

Two positive point charges of and are place at a distance away from each other, as shown below. If a positive test charge, , is placed in between, at what distance away from will this test charge experience zero net force?

**Possible Answers:**

**Correct answer:**

To find the location at which the test charge experience zero net force, write the net force equation as , where is the force on the test charge from , and is the force on the same test charge from . Using Coulomb's law, we can rewrite the force equation and set it equal to zero.

In this equation, the distance, , is how far away the test charge is from , while represents how far away the test charge is from . Now, we simplify and solve for .

Cross-multiply.

We can cancel and . We do not need to know these values in order to solve the question.

Now that we have isolated , we can plug in the values given in the question and solve.

### Example Question #1 : Using Coulomb's Law

You are standing on top of a very large positively charged metal plate with a surface charge of .

Assuming that the plate is infinitely large and your mass is , how much charge does your body need to have in order for you to float?

**Possible Answers:**

**Correct answer:**

Consider the forces that are acting on you. There is the downward (negative direction) force of gravity, . In order for you to float, there has to be an upward (positive direction) force, and that upward force is coming from the metal plate, . To show that you would float, the net force equation is written as , where is the charge on you.

For plates that are charged, know that .

Knowing this, the force equation becomes .

Solve for .

Now we can plug in our given values, and solve for the charge.

### Example Question #1 : Electricity And Magnetism Exam

A point charge of exerts a force of on another charge with . How far apart are the two charges?

**Possible Answers:**

**Correct answer:**

To find the distance between the two charges, use Coulomb's Law.

Since we want to find distance, , we solve for .

We know the values of the force and the two charges.

We can plug in these values and solve for the distance.

### Example Question #1 : Electricity And Magnetism Exam

What is the electric force between two charges, and , located apart?

**Possible Answers:**

**Correct answer:**

The equation for finding the electric force between two charges is , where . Using this, we can rewrite the force equation.

Now, we can use the values given in the question to solve for the electric force between the two particles.

### Example Question #1 : Electricity And Magnetism Exam

What is the magnitude of the electric field at a field point from a point charge of ?

**Possible Answers:**

**Correct answer:**

The equation to find the strength of an electric field is .

We can use the given values to solve for the strength of the field at a distance of .

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