# AP Physics 1 : Fundamentals of Electric Charge

## Example Questions

### Example Question #1 : Fundamentals Of Electric Charge

A point charge of charge  is placed in a uniform electric field of strength going to the right. The charge is then moved  at an angle of  below the horizontal to the right. What is the net work done on this charge?

Explanation:

The work done by an electric field on a charged particle is:

Where  is the angle between the electric field vector and the displacement vector. Plug in the given values.

This answer makes sense since an electric field does work on a positive charge when going in the direction of the field lines.

### Example Question #2 : Fundamentals Of Electric Charge

Two charges of  and  are placed  away from each other. Another charge is placed in between these two charges. Where should this third charge be placed in order for it to feel no net electrostatic force?

from the  charge

from the  charge

from the  charge

from the  charge

There is not enough information given in this problem to solve the question

from the  charge

Explanation:

The electrostatic force between two charges is:

The force that the 3rd charge feels from the  charge is:

The force that the 3rd charge feels from the  charge is:

We can also rewrite the distance between the charges as  and . In this explanation, we will use  as the distance between the  and the third unknown charge making the distance between the  and the 3rd charge . Finally, we solve for a net force of 0 giving us this relationship between the two opposing forces.

Solve for .

### Example Question #3 : Fundamentals Of Electric Charge

A student has a neutrally charged glass rod and a neutrally charged silk cloth. When the student rubs the silk cloth on the glass rod, the rod acquires a net positive charge. What is the charge on the silk cloth after the student performs this experiment?

The silk cloth has the same charge as the glass rod

The silk cloth is positively charged and has a greater magnitude of charge than the glass rod.

The silk cloth has no charge

The silk cloth is negatively charged and has a smaller magnitude of charge than the glass rod

The silk cloth has a charge that is equal in magnitude to the glass rod's charge, but is negative

The silk cloth has a charge that is equal in magnitude to the glass rod's charge, but is negative

Explanation:

Charge is fundamentally conserved. In order to give the glass rod a positive charge, the silk cloth removes electrons from the glass rod. Every electron that leaves the glass rod leaves behind the proton (positively charged particle) that used to balance the negative charge of the electron (negatively charged particle). Every electron that leaves the glass rod goes onto the silk cloth, giving it the same amount of charge as the glass rod, but with a negative sign (since electrons are negatively charged). Only a tiny fraction of the total electrons in the glass rod are removed, even with vigorous charging.

### Example Question #4 : Fundamentals Of Electric Charge

If the test charge is increased by a factor of 4, what happens to the electric potential of that charge?

Increases by a factor of

Decreases by a factor of

Decreases by a factor of

Remains unchanged

Remains unchanged

Explanation:

Remember that the formula for the electric potential is given by:

Where  is Coulomb's constant,  is the source charge, and  is the distance. This formula indicates that electric potential is unaffected by changing the test charge.

### Example Question #5 : Fundamentals Of Electric Charge

By how much will the electric field change if the charges of all source charges are increased by a factor of , and the test charge is increased by a factor of

The electric field will be changed by a factor of

The electric field will be changed by a factor of

The electric field will be changed by a factor of

The electric field will be changed by a factor of

The electric field will be changed by a factor of

Explanation:

The electric field  for point charges is given by:

Where  is Coulomb's constant,  is the charge of each source charge , is distance of the test charge from the source charge, and  is the number of source charges.

In this problem, since all of the source charges are increased by a factor of 2, the electric field will also increase by a factor of 2. The increase in the charge of the test charge is not applied to the strength of the electric field, since the electric field is only dependent on the values and locations of the source charges.

### Example Question #6 : Fundamentals Of Electric Charge

Two identical conducting spheres are attached to insulated posts and charged so that  and .

The spheres are brought together so they touch, then moved back apart. What is the charge on  now?

Explanation:

When the spheres make contact, charges are exchanged. The charges on the spheres will move due to the Coulomb forces from all the particles in each sphere. They will move toward equilibrium.

In this case  has a net negative charge while  has a net positive charge.  will have to migrate to  so that .

When the spheres are separated they will have equal charge and the charge on  will still be .

### Example Question #7 : Fundamentals Of Electric Charge

Determine the total electric charge of   molecules in solution in Coulombs.

Explanation:

In solution, the ions will disassociate into  and . Since there will be  molecules of  with a total charge  and  molecules of  with a total charge of , the overall charge will be

### Example Question #8 : Fundamentals Of Electric Charge

Consider the given diagram of two electrical charges. Which of the following is true about charges A and B?

A is positive and B is negative

Both charges are negative

Both charges are positive

A is negative and B is positive

Both charges are positive

Explanation:

In this question, we're presented with a diagram in which two electrical charges have field lines pointing away from them. We're then asked to determine a true statement regarding these two charges.

To be able to answer this question correctly, we'll have to recall that for positive electrical charges, the field lines will always point away from the charge. For negative electrical charges, the field lines point inwards toward the charge. Since both charges A and B in the diagram have their field lines pointing away from them, both of them must be positively charged. Also notice that their field lines will not cross one another; instead, they are repelled from one another.

### Example Question #9 : Fundamentals Of Electric Charge

An electric field line is point from the left towards the right. Where will an electron move when placed in the field?

Towards the left

Towards the right

Downward

It will not move

Upward

Towards the left

Explanation:

The electron will move towards the left because electric field lines always point towards the negative charge. The electron is negatively charged and will oppose the negative electric field on the right and move towards the positive end on the left.

Therefore the correct answer is that the electron will move to the left.

### Example Question #10 : Fundamentals Of Electric Charge

A point charge of  coulombs experiences a force of  in an electric field. What is the magnitude of this electric field?

Explanation:

The formula for the force on a point charge in an electric field is as follows:

is the force on the charge,  is the magnitude of the charge and  is the electric field. Substituting for our values we obtain: