Electric Force Equation | Calculating Electric Forces, Fields & Potential – Video & Lesson Transcript | Study.com

Video Transcript

Electric Force

Imagine a very small room with two people. There might be tension, causing them to stay away from each other, or they could be best friends, causing them to stick close together. What connections exist between them? What would it take to get another person to hang out in this room?

These are analogies regarding the interactions with point charges. Let’s learn how to calculate forces, electric fields, and electric potentials all exerted from a congregation of charges.

The two people in our room may move towards or away from each other based on their personalities. This will depend on whether they have a positive or negative ”charge.”

Let’s take a look this diagram right now:

Force is a push or pull on something. What force do these charges feel from each other? Did you know we can calculate the actual force applied to each charge using Coulomb’s law? Coulomb’s law reads as:

Coulomb

where:

• |F

  E

  | is the magnitude of the electric force in newtons (N)

• k is Coulomb’s constant, equal to 8.99 x 10

  9

  newton-meters-squared-per-coulomb squared (N⋅m

  2

  /C

  2

  )

• q

  1

  and q

  2

  are the charge magnitudes (strengths) in coulombs (C)

• r is the distance between the charges in meters (m)

Based on the scenario in our first diagram , the force between the charges is calculated as follows:

The force given in the example is an attractive force because the charges are opposite in sign. This is just like the opposite ends of magnets attracting each other.

Electric Field

Electric charges can also produce electric fields. An electric field is what emanates from a charged particle into the space surrounding it. A single charge generates a standard electric field, while more than one charge field combines to create a ”net” electric field. Electric fields point away from positive charges in all directions, and they point towards negative charges in all directions.

The diagram shows the net electric field generated by the two charges:

Electric fields are similar to the connections between the two people in our room. Do their interests point in the same direction, or are they opposed to each other? Would a new person in the room move towards the person on the left or the right, based on their interests?

If a small test charge was placed in the electric field from our scenario, it would move along the field lines. If the test charge was positive, it would move with the direction of the net electric field, and if negative, it would move against the direction of the net electric field.

Let’s calculate the net electric field at 1.5 mm away from both charges, designated by the X in this diagram:

The electric field equation is:

where:

• |E| is the magnitude of the electric field in newtons-per-coulomb (N/C)
• q is the magnitude of the charge in coulombs
• k is Coulomb’s constant
• r is the distance from the charge in meters (m)

We have two charges, so we first have to determine the electric field generated by both of them, and then do vector addition. We will ignore the signs on the charges until the magnitude is determined. We will then decide if the field is positive or negative based on which way the electric field points at the X. We’ll start with charge 1 (q1):

(Charge one is positive so we have given the it a positive sign.)

Next, we will calculate the electric field that occurs due to charge 2 (q2):

(Charge 2 is negative so we have put a negative sign on it.)

When adding vectors, we make sure to add components in the same direction. Adding the electric fields together, we get:

Electric Potential

Electric potential is the energy-per-unit charge, also known as voltage (V). Voltage is the ”push” that moves the new person who entered our room towards or away from a specific location, based on the charges between the two original people.

Electric charges move because of a difference in voltage. This is called potential difference, which represents how batteries work. We can calculate the electric potentials of each of our point charges at the midpoint between them.

The voltage formula is:

• V is voltage in volts (V)
• k is Coulomb’s constant
• q is the charge in question
• d is the distance from the charge, q

To calculate the voltage at the midpoint, we must determine the voltages for each charge and simply add them because they are not vectors. The voltage from q1 at the midpoint is:

and from q2 is:

and the net voltage is:

If an electric field is constant, voltage is the product of the electric field and the distance between the charges.

Lesson Summary

Let’s review…

When more than one charge is present, an electric force exists. Force is the push or pull on an object and is a vector. If the charges are opposite in sign, they attract. If charges are the same sign, they repel each other. This is easily imagined when you think about how magnetic poles react to each other. Since force is a vector, the net force equals the vector addition of all forces between charges.

An electric field is also a vector, and emanates from a charged particle into the space surrounding it. Electric field lines move away from positive charges and towards negative ones. If there are any other charges in the vicinity of the original charges that formed the electric field, they will move along the field lines. The magnitude of an electric field is similar to the electric force equation, but it only includes one charge instead of two.

Another aspect of electric charge is electric potential, which is energy-per-unit-charge; also known as voltage. Voltage can be calculated for each charge based on the distance from the charge. It’s also important to note that it isn’t a vector.

Voltage is also the product of a constant electric field and distance between the charges.