First, let's calculate the electric field at C due to point A.

We can tell that the net electric field will be in the  direction.

 in the  direction.

Use the equation to find the magnitude of an electric field at a point.

Solve.

Since it is a positive charge, the electric field lines will be pointing away from the charged particle.

We will need to use the electric field equation, twice. Because we are given coordinates, we will need to use vector notation.

Combine the two equations.

Plug in known values. 

Note that the charge is positive. This is because the electric field lines point towards the negative charge at the origin, and in order to balance this at your location, the electric field lines of the charge at (0,-3) must be pointing away from the charge.

Potential is not a vector, so we just add up the two potentials and set them to each other. The equation for electric potential is:

If the point we are looking for is distance  from , it's  from . Cancel all the common terms, then cross-multiply:

Since we had  associated with , it's from that charge toward the weaker charge.

Electric field is a vector. In between the charges is where 's field points right and 's field points left, so somewhere in between, the two vectors will add to zero. It will be closer to the weaker charge, , but since field depends on the inverse-square of the distance, it will not be linear, and we'll have to do some math.

First set the magnitudes of the two fields equal to each other. The vectors point in opposite directions, so when their magnitudes are equal, the vector sum is zero.

Many of the terms cancel, making it a bit easier. Now cross multiply and solve the quadratic:

Using coulombs law to solve

 Where:

 it the first charge, in coulombs.

 is the second charge, in coulombs.

 is the distance between them, in meters

 is the constant of 

Converting  into 

Plugging values into coulombs law

Magnitude will be the absolute value

Using the electric field equation:

Where is 

is the charge, in

is the distance, in .

Convert  to and plug in values:

Magnitude is equivalent to absolute value:

Using the electric field equation:

Where is 

is the charge, in

is the distance, in .

Convert  to and plug in values:

Magnitude is equivalent to absolute value:

Use the electric field equation:

Where is 

is the charge, in

is the distance, in .

Convert  to and plug in values:

Magnitude is equivalent to absolute value:

To solve this question, we need to recall the equation for electric field strength.

Notice that the equation above represents an inverse square relationship between the electric field and the distance between the source charge and the point of space that we are interested in.

Plug in the values given in the question stem to calculate the magnitude of the electric field.

Now that we have determined the magnitude of the electric field, we need to identify which direction it is pointing with respect to the source charge. To do this, we'll need to remember that electric fields point away from positive charges and towards negative charges. Therefore, since our source charge is positive, the electric field will be pointing away from the source charge.