Electric Field Strength

Electric field strength: Interaction between electric fields

Another way in which an electric field differs from a gravitational field is that an electric field can have a positive or a negative direction. A gravitational field, on the other hand, only has a positive direction. This is a convenient way to compute the direction of a field at any instant in free space.

The more densely packed the field lines, the stronger the field. Field lines are also useful if many charges are interacting with one another. Figure 3 is an example of an electric dipole, as the charges are opposite.

Electric field strength formula

We can measure an electric field generated via a point charge by calculating its electric field strength. Electric field strength is a force exerted by a +1 C charge (test charge) when it is placed in an electric field.

\[E = \frac{F}{Q}\]

Here, E is the electric field strength measured in Newtons/Coulombs, F is the force in Newtons, and Q is the charge in Coulombs.

The field strength primarily depends on where the charge is located in the field. If a charge is located where the field lines are dense, the experienced force will be stronger. It should be noted that the above equation is valid for linear fields.

We will assume charges as point charges, meaning that all the charge is concentrated at the centre and has a radial field.

In a radial electric field, the electric field strength can be represented as:

\[E = K_c \frac{Q}{r^2}\]

Here:

• E is the electric field strength measured in Newtons per Coulomb.
• K_c is the Coulomb constant with a value of 8.99⋅10⁹.
• Q is the point charge in Coulombs.
• r is the distance from the point charge in metres.

Electric field strength follows an inverse square law: if the distance from Q increases, the strength of the field decreases.

How can we use an electric field?

If we take two charged plates and apply a voltage across them, with one of them having a positive and the other a negative charge, then in between the plates, an electric field will be induced that is parallel and uniformly distributed.

As the electric field strength is the force experienced by a 1 C charge, the force acting on a positively charged particle can be taken as being equal to the potential difference applied across the plates. Hence, for the example in figure 5, the electric field strength equation is:

\[E = \frac{V}{d}\]

Here, E is the electric field strength (V/m or N/C), V is the potential difference in Volts, and d is the distance between the plates in metres.

So, if we put a test charge in a uniform electric field, it is going to experience a force towards the negative end of the terminal or plate. And as this field happens to be uniform, the electric field strength will be the same regardless of where inside the field the test charge is put.

Electric field strength: A test charge entering a uniform field with a velocity

The above scenario is for a test charge placed inside a uniform electric field. But what if a charge enters an electric field with an initial velocity?

If a charge enters a uniform electric field with some initial velocity, it will bend, with the direction depending on whether the charge is positive or negative.

A charge that enters at a right angle to the field feels a constant force that acts parallel to the field lines inside the plates. In figure 7, a positively charged particle enters a uniform electric field at a right angle and flows in the same direction as the field lines. This causes the positive charge to accelerate downward in a curved parabolic path.

If the charge is negative, the direction will be in the opposite direction to the field lines.