Electric Field Formula: Derivation & Solved Examples

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Electric Field refers to the surrounding region produced by an electric charge whose influence is observed when another charge is brought into the electric field region. It is created when there is an electric charge around a region, and its effect can be observed when another charge is brought into a region where the electric field is. The electric field can be denoted using units Volts per metre (V/C) or Newtons per Coulomb (N/C).

The magnitude of an electric field can be calculated by the Electric field formula E = F/q

where E is the electric field,
F is the force acting on the charge,
q is the charge surrounded by its electric field

The electric field formula can also be represented as E = k|Q|/r². The sign of the charge determines the direction of the electric field.

Table of Content

What is Electric Field?
Electric Field Formula
Unit of Electric Field
Application of Electric Field
Things to Remember
Previous Year Questions
Sample Questions

Key Terms: Electric Field, Electric Charge, Electrical Force, Intensity, Charge, Distance, Coulomb, Current, Volts

What is Electric Field?

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Electric Field is the region that is formed around a charge. When another charge is brought into the region of an electric field, its influence can be observed.

The electric field created will either repel or attract the charge.
The strength and intensity of the electric field are determined by the electrical force and charge of that field.
If the charge is represented by q and the force is denoted by F, then the direction of the field lines is determined by both F and q.
An electric field is a vector quantity with arrows going toward or away from charges.

Electric field

Electric Field

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Physical Significance of Electric Field	Electric Charges and Fields MCQ	Electric Field Formula

Electric Field Formula

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Electric Field Formula is E = F/q

E = \(F \over q\)

In the above equation, E is the electric field,
F is the force acting on the charge,
and q is the charge surrounding the electric field.

If two charges, Q and q, are separated from each other by a distance r, then the electrical force can be described as,

F = k Qq/qr²

Where, F is the electrical force
Q and q are the two charges
R is the distance of separation of the two charges
K is Coulomb’s constant.

Let the two charges be Q and q, and let the distance between them be r.

So, in the above case:

\(E = {KqQ \over r^2q}\)

If a voltage is supplied across the distance between the two charges, then the electric field formula is given by-

Electric field formula (E) = V/r

Solved Examples

Example 1: A force of 5 N is acting on the charge 6 μ C at any point. Find out the electric field intensity at that point.
Solution: Given

Force F = 5 N

Charge q = 6 μ C

The electric field formula is given by

E = F / q

= 5N / 6×10⁻⁶C

E = 8.33 × 10⁵ N/C.

Example 2: A rectangular loop has dimensions of 0.50m and 0.60m, and the values of B are 0.02T and 45°, respectively. Determine the magnetic flux at the surface.

Solution: Given:

Dimensions of rectangular loop = 0.50m and 0.60m,

B = 0.02T

θ = 45°

Magnetic flux formula is given by

ΦB = B A Cosθ

Area, A = 0.50 × 0.60

= 0.3 m2

ΦB = 0.02 × 0.3 × Cos 45

ΦB = 0.00312 Wb

Unit of Electric Field

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The standard Unit of Electric Fields is Volts per metre (V/C). The electric field can also be denoted using N/C. This is equivalent to Newton’s per Coulomb.

Applications of Electric Field

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Electric fields have various applications:

Electric fields are used in the study of tissue dynamics.
Electric fields are used in the process of electroporation to create pores in the cell membranes to pass drugs, genes, or medicines. Cloning processes involve the use of electroporation.
Various Crystallization processes such as crystal growth and nucleation can be controlled using electric fields.

Also read: Dipole in a Uniform External Field

Things to Remember

Electric Field is created when there is an electric charge around a region.
When another charge is brought into the region where the electric field is, its influence can be observed.
The electrical force and the electrical charge determine the intensity of the electric field.
Electric field can be denoted using the units of Volts per metre (V/C) or Newton’s per Coulomb (N/C).
Electric Field formula, E = Fq , where F is force and q is charge.
Electric field (E) = Vr, where V is voltage and r is distance.

Also read:

Related Topics
Electric Charges and Fields	Electric Dipole	Maxwell's Equations
Electrostatics	Electroscope	Electrical Insulators
Continuous Charge Distribution	Conservation of Charge	Gaussian Surface

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Sample Questions

Ques 1. What is electric field intensity for a force of 60 N acting on a charge of 12 C? (2 Marks)

Ans. In the above equation,

Force (F) = 60 N

Charge (q) = 12 C

Electric field (E) = F/q

Electric field (E) = 60/12

Electric Field (E) = 5 N/C

Ques 2. What is the electric field intensity for a force of 42 N acting on a charge of 7 C? (2 Marks)

Ans. In the above equation,

Force (F) = 42 N

Charge (q) = 7 C

Electric field formula (E) = F/q

Electric field (E) = 42/7

Electric Field (E) = 6 N/C

Ques 3. What is the electric field strength for a Voltage of 90 V acting across a distance of 10 m? (2 Marks)

Ans. In the above equation,

Voltage (V) = 90 V

Distance (r) = 10 m

Electric field (E) = V/r

Electric field (E) = 90/10

Electric Field (E) = 9 V/m

Ques 4. If the electric field intensity acting on a charge of 3 C is 7 N/C, what is the electrical force? (2 Marks)

Ans. In the above equation,

Charge (q) = 3 C

Electric field (E) = 7 N/C

Electric field formula (E) = F/q

So, Force (F) = Eq

Force (F) = 7 x 3 N

Force (F) = 21 N

Ques 5. If the electric field intensity for a force of 30 N is 5 N/C, what is the electrical charge? (2 Marks)

Ans. In the above case,

Electric field (E) = 5 N/C

Force (F) = 30 N

Electric field (E) = F/q

So, Charge (q) = F/E

Charge (q) = 30/5

Charge (q) = 6 C

Ques 6. Write a note on Conductors and Insulators. (3 Marks)

Ans. Conductors: Materials that allow electricity to pass through them are electrical conductors. Conductivity is a property of electrical conductors. The electric charge is distributed across the surface equally. When a conductor with a charge comes in contact with another conductor with no charge, a transfer of charges takes place. Some examples of conductors are iron, gold, steel, etc.

Insulators: Materials that disturb or hinder the free flow of electric charge are known as insulators. If we pass an electric charge through insulators, the charge does not distribute itself but rather stays at the initial position. Such elements can be charged through induction. Some examples of insulators are wood, plastic, rubber, etc.

Ques 7. Write a note on Electric Charge. (3 Marks)

Ans. When the matter is kept in a magnetic or electric field, the force it experiences is called an Electric Charge. When the electric charge is moving, it generates a magnetic field. When electric fields and magnetic fields are combined, it is known as an electromagnetic field.

Electric Charges are of two types: Positive and Negative. These charges are carried by protons and electrons. Protons carry a positive charge whereas electrons carry a negative charge.

Electric charge is a scalar quantity. An electric charge possesses direction and magnitude, but it does not follow the laws of vector addition, hence it is a scalar quantity. The SI unit of electric charge is Coulomb.

Ques 8. What are the properties of Electric Charge? (4 Marks)

Ans. The three basic properties of Electric charge are:

Additivity of Electric Charge

If a system of charge contains three point charges with three different magnitudes, the total charge will be the sum of all three charges. These charges can be positive or negative. Electric charges are scalar quantities.

Conservation of Electric Charge

Electric charges can neither be created nor destroyed. For example, if a body with some charge comes in contact with a body with no charge, the charge will be transferred and equally distributed among the objects. Hence charge cannot be created or destroyed, just transferred.

Quantization of Electric Charge

The principle of quantization of electric charge stated that all the free charges are integral multiples of a basic already defined unit.

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Electric Field Formula: Derivation & Solved Examples

What is Electric Field?

Electric Field Formula

Solved Examples

Unit of Electric Field

Applications of Electric Field

Things to Remember

Previous Year Questions

Sample Questions

CBSE CLASS XII Related Questions

1.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

2.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

4.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

6.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

Electric Field Formula: Derivation & Solved Examples

What is Electric Field?

Electric Field Formula

Solved Examples

Unit of Electric Field

Applications of Electric Field

Things to Remember

Previous Year Questions

Sample Questions

CBSE CLASS XII Related Questions

1. If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

2.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

4. If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

6.What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

2.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

3.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

4.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

6.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?