[Physics Class Notes] on Calculating the Value of an Electric Field Pdf for Exam

Electricity is one of the critical topics in the field of physics. It is also important in our day-to-day lives. While gaining sound knowledge on electricity, several new Concepts have come across like the electric field, magnetic field, electrons, protons, etc., and many more. Among all those topics, learn and understand about the electric field. Also, know how to calculate the value of an electric field?

Electric Field Definition

The electric field is a field in which each point of the field has either a positive charge or negative charge by exerting some force. As every item consists of both charges in the form of a nucleus and electrons, they attract or repel with other particles of an atom. This process can be done either through electric fields or through magnetic fields.

How to Calculate the Value of an Electric Field

For calculating the value of an electric field, different formulas are available based on the requirement. 

If the value is required in terms of charge point and distance, 

E= K*(Q/r²)

Derivation

To derive the formula for the electric field, let’s recall Coulomb’s law of equations.

According to Coulomb’s law, the electric force existing between two different charges is always directly proportional to the product of these two charges and inversely proportional to the square of the distance between those two charges. 

Let us assume that Q, q are two different charges. Where capital Q is the source charge and q is the test charge. And r is the distance between those two charges. Applying these variables in Coulomb’s law in the formula of electric force we get,

F = K(Q*q)/r²

As we know that the magnitude of an electric field is defined as the force per charge, 

E = F/q

Here the charge can be taken as a test charge.

Now substitute the force formula in the electric field formula.

E =K [(Q*q)/r²]/q

Then the test charge will be canceled from the numerator and denominator.

Hence the obtained formula for the magnitude of electric field E is,

E = K*(Q/r²)

Where,

        E is the magnitude of an electric field,

        K is Coulomb’s constant

        Q is the charge point,

        r is the distance from the point,

Similarly, if we need to calculate the value of an electric field in terms of electric potential, the formula is,

E= – grade.

It is a vector calculus notation. According to the definition of an electric field, it is always equal to the negative gradient of electric potential. By considering this definition, the above formula was derived.

Concerning the given data, it is easy to calculate the value of the electric field in terms of distance and the charge as well as electric potential. Both of these formulae were used to solve physics word problems also.

Units and Direction of Electric Field

The magnitude of electric field E is measured in terms of Volts per meter, an SI system unit.

The direction of the electric field will be outwards for positively charged particles and inwards for negatively charged particles. Usually, it flows in the direction of a positive charge.

Using Gauss law

Let’s see how to calculate the value of an electric field using Gauss law. The procedure is simple and straightforward with few steps.

• First, we need to find a spatial symmetry that may be either spherical, linear circular, etc. for charge distribution.

• Next, take a gaussian symmetry which is similar to that of the spatial symmetry.

•  Let’s find integral [varphi] SE and then flux.

• Now the charge is enclosed by the whole surface.

• Let’s find that electric field using formulae which may vary by the shape of the spatial symmetry. 

Conclusion

Hence, the electric field is a charge distributed to each point of the field by exerting some force on both positive and negative particles. It can be determined and calculated by various factors. Also, it has various specifications in terms of deriving formulas in different cases. The magnitude of the electric field is measured using Volts per meter. The electric potential, charge distribution, distance between two charges, etc. were considered a major league. The electric field can be calculated at a single point to charge and the charge between two or more points.