Electric Fields - AP Physics 2

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

Use the electric field equation:

Where is

is the charge, in Coulombs

is the distance, in meters.

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:

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 Coulombs

is the distance, in meters.

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:

Use the electric field equation:

Where is

is the charge, in Coulombs

is the distance, in meters.

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.

Using electric field formula:

Converting to , to and plugging in values:

Using electric field formula:

Converting to , to and plugging in values:

Using

Plugging in values:

In this question, we are given the strength of an electric field at a given distance away from a source charge. Then, we're asked to find what the strength of this electric field would be at a different distance away from the source charge.

First, we will need to use the equation for the electric field.

Since we're given the strength of the electric field at a distance of away, we can use this information to solve for the value of .

Now that we have the value for , we can use it to find the value of the electric field from the source charge.

Using Coulomb's law:

Where

is the distance, in meters,

and is the charge, in Coulombs.

Plugging in values:

The positive sign indicates that the field is pointing away from the charge.

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.