What is an Electric Field Intensity : Formula and Calculations

All the materials are made up of atoms which contains subatomic particles such as electrons, protons, and neutrons. These sub-atomic particles are also known as charged particles. Electrons have a negative charge whereas protons are positively charged. If an atom contains a large number of electrons compared to the number of protons, it is said to be negatively charged. Whereas if an atom contains a large number of protons compared to the number of electrons, it is said to be positively charged. Every electric charge has an electric field associated with it. One of the characteristics of an electric charge is the Electric Field Intensity.

What is Electric Field Intensity?

Definition: Electric charge is carried by the subatomic particles of an atom such as electrons and photons. The charge of an electron is about 1.602×10^-19 coulombs. Every charged particle creates a space around it in which the effect of its electric force is felt. This space around the charged particles is known as the “Electric field“. Whenever a unit test charge is placed in this electric field it will experience the force emitted by the source particle. The amount of force experienced by a unit charged particle when it is placed in the electric field is known as Electric field intensity.

Electric Field Intensity is a vector quantity. It has both magnitude and direction. The test charge that is subjected to the electric field of the source charge, will experience force even if it is in a rest position. The electric field strength is independent of the mass and velocity of the test charge particle. It only depends on the amount of charge present on the test charge particle. The test charge can be either a positively charged particle or a negatively charged particle.

The direction of the electric field is determined by the charge on the test charge particle. For deriving the direction of electric field intensity, the test charge is considered to be a positive charge. So, when a positive test charge particle is introduced to this electric field it will experience a repulsion force. Thus, the electric field strength will be directed in the direction away from the charge. Whereas for a negatively charged test charge the direction of force for electric field strength will be towards the source charge particle.

Electric Field Intensity Formula

Let us consider a charged particle with charge ‘Q’. This charged particle creates an electric field around it. Since this charged particle is the source of the electric field, it is referred to as a source charge. The strength of the electric field created by the source charge can be calculated by placing another charge in its electric field. This external charge particle which is used to measure the electric field strength is called the test charge. Let the charge on the test charge be ‘q’.

When a test charge is placed in the electric field it will experience either an attractive electric force or a repulsive electric source. Let the force be denoted by ‘F’. Now, the magnitude of the electric field strength can be defined as ” the force per charge on the test charge”. Thus, the electric field intensity ‘E’ is given as

E = F/q——Eqn1

Here, the charge on the test charge particle is considered rather than the charge on the source charge particle. When considered in SI units the units of electric field intensity are Newton per coulombs. The electric field intensity is independent of the amount of charge on the test charge particle. It is measured the same all around the source charge regardless of the charge of the test charge particle.

From Coulomb’s Law

Electric field intensity is also known as the electric field strength. The formula for electric field strength can also be derived from Coulomb’s law. This law gives the relation between the charges of the particles and the distance between them. Here, the two charges are ‘q’ and ‘Q’. Thus, the electric force ‘F’ is given as

F = k.q.Q/ d²

where k is the proportionality constant and d is the distance between the charges. When this equation is substituted for force in equation 1, the formula for electric field intensity is derived as

E= k. Q/d²

The above equation shows that the electric field intensity is dependent on two factors – the charge on the source charge ‘Q’ and the distance between the source charge and test charge.

Thus, the electric field intensity of a charge is location dependent. It is inversely proportional to the square of the distance between source charge and the test charge. As the distance increases the magnitude of the electric field strength or electric field intensity decreases.

Calculations of Electric Field Intensity

From the formula of electric field intensity, it was derived that-

• It is inversely proportional to the distance between the source and test charges.
• Directly proportional to the charge ‘Q’ on source charge.
• Not dependent on the charge on the test charge ‘q’.

When these conditions are applied to the inverse square law, the relation between the electric field strength (E1) at a distance d1 and the electric field intensity (E2) at distance (d2) is given as-

E1/E2 = d²1/d²2

Thus, when the distance is increased by the factor of 2, the electric field intensity will decrease by the factor of 4.

Calculate the electric field strength acting on a particle with charge -1.6×10^-19 C when the electric force is  5.6×10^-15N.

Here, the force F and the charge ‘q’ are given. Then the electric field strength E is calculated as E = F/q

thus, E = 5.6×10^-15 /-1.6×10^-19 = -3.5×10⁴ N/C

The dimensional formula for force(newton) for the unit kg.m/s² is MLT^-2. The dimensional formula for coulomb for ampere-sec is AT. Thus, the dimensional formula for electric field strength is MLT^-3A^-1.

FAQs

1). How is the electric field defined?

The electric field is defined as the force per unit charge.

2). What is the value of the proportionality constant ‘k’?

The value of the proportionality constant ‘k’ in coulomb’s law is 9.0×10⁹ N.m²/C².

3). Does electric field strength depend on the quantity of charge on the test charge?

No, the electric field strength does not depend on the quantity “q”. According to coulomb’s law as the charge increases, the electric force also increases by the same factor. Thus, these two changes cancel out each other. This can be understood by the formula of the electric field strength, E = F/q.

4). What is the direction of electric field strength when the positively charged test particle is used?

When the positive charges particle is used, the electric field intensity vector will always be directed away from the positively charged objects. Because as both the source charge and test charge are of positive charge, they repel each other. This is vice-verse for negatively charges particles.

Thus, things get difficult when the point charge is placed under the influence of many source charges. Here, initially, the electric field strength of individual source charges are calculated. Then, the vector sum of all these intensities gives the resultant field strength at that point charge. What is the direction of the electric field strength when the test charge is negative?