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 

First we need to calculate the equivalent resistance of the circuit using the following expression for condensing parallel resistors:

Now we can use Ohm's law to calculate the current flowing through the circuit:

First, identify the given information:

Two equations are required for this problem:

1.) Ohm's law, 

2.) Electrical power

Using the equation for electrical power, we can rearrange to solve for :

At this point, we can substitute in the known values and determine the voltage:

Ohm's law can then be rearranged to solve for the resistence of the light bulb:

The known voltage value then can be substituted into Ohm's law to determine the resistance of the light bulb:

Use Ohm's law.

Plug in known values and solve for resistance.