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.

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 .

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.

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. 

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. 

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 .

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 

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.

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. 

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:

Therefore the correct answer is