# AP Physics C Electricity : Electricity

## Example Questions

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

Two capacitors are in parallel, with capacitance values of  and . What is their equivalent capacitance?

Explanation:

The equivalent capacitance for capacitors in parallel is the sum of the individual capacitance values.

Using the values given in the question, we can find the equivalent capacitance.

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

A proton moves in a straight line for a distance of . Along this path, the electric field is uniform with a value of . Find the force on the proton.

The charge of a proton is .

Explanation:

The force of an electric field is given by the equation , where is the charge of the particle and is the electric field strength. We can use the given values from the question to solve for the force.

### Example Question #3 : Using Coulomb's Law

Two point charges,  and  are separated by a distance .

The values of the charges are:

The distance is 4.0cm. The point  lies 1.5cm away from  on a line connecting the centers of the two charges.

What is the magnitude and direction of the net electric field at point  due to the two charges?

Explanation:

At point , the electric field due to  points toward  with a magnitude given by:

At point P, the electric field due to Q2 points away from Q2 with a magnitude given by

The addition of these two vectors, both pointing in the same direction, results in a net electric field vector of magnitude 152000 volts per meter, pointing toward .

### Example Question #11 : Electricity

A charge, , is enclosed by two spherical surfaces of radii  and , with . The cross-sectional side view is shown.

Which is the correct relationship between the electric flux passing through the two spherical surfaces around the point charge?

Explanation:

Electric flux is given by either side of the equation of Gauss's Law:

Since the charge is the same for both spherical surfaces, even though these surfaces are of different radii, the amounts of electric flux passing through each surface is the same.

### Example Question #1 : Calculating Electric Potential

A proton moves in a straight line for a distance of . Along this path, the electric field is uniform with a value of . Find the potential difference created by the movement.

The charge of a proton is .

Explanation:

Potential difference is given by the change in voltage

Work done by an electric field is equal to the product of the electric force and the distance travelled. Electric force is equal to the product of the charge and the electric field strength.

The charges cancel, and we are able to solve for the potential difference.

### Example Question #1 : Calculating Electric Potential

For a ring of charge with radius  and total charge , the potential is given by .

Find the expression for electric field produced by the ring.

Explanation:

We know that .

Using the given formula, we can find the electric potential expression for the ring.

Take the derivative and simplify.

### Example Question #1 : Calculating Electric Potential

The potential outside of a charged conducting cylinder with radius  and charge per unit length  is given by the below equation.

What is the electric field at a point located at a distance from the surface of the cylinder?

Explanation:

The radial electric field outside the cylinder can be found using the equation .

Using the formula given in the question, we can expand this equation.

Now, we can take the derivative and simplify.

### Example Question #1 : Calculating Electric Potential

A proton moves in a straight line for a distance of . Along this path, the electric field is uniform with a value of . Find the work done on the proton by the electric field.

The charge of a proton is .

Explanation:

Work done by an electric field is given by the product of the charge of the particle, the electric field strength, and the distance travelled.

We are given the charge (), the distance (), and the field strength (), allowing us to calculate the work.

### Example Question #1 : Calculating Electric Potential

A negative charge of magnitude  is placed in a uniform electric field of , directed upwards. If the charge is moved  upwards, how much work is done on the charge by the electric field in this process?

Explanation:

Relevant equations:

Given:

First, find the potential difference between the initial and final positions:

2. Plug this potential difference into the work equation to solve for W:

### Example Question #1 : Calculating Electric Potential

Three point charges are arranged around the origin, as shown.

Calculate the total electric potential at the origin due to the three point charges.