Electric Field Due To A Uniformly Charged Infinite Plane Sheet

Definition of Electric Field

An electric field is defined as the electric force per unit charge. It is given as:

E = F/Q

Where,

  • E is the electric field
  • F is the force
  • Q is the charge

The variations in the magnetic field or the electric charges are the cause of electric fields. Volt per meter (V/m) is the SI unit of the electric field.

Definition of Gaussian Surface

A Closed Surface in a three-dimensional space whose flux of a vector field is calculated, which can either be the magnetic field or the electric field or the gravitational field, is known as the Gaussian Surface.

Gaussian surface formula

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What is Electric Field Due to a Uniformly Charged Infinite Plane Sheet?

Electric field due to a uniformly charged infinite plane sheet

Let us consider an infinitely thin plane sheet that is uniformly charged with a positive charge. Let 𝜎 be the charge density on both sides of the sheet. At point P the electric field is required which is at a distance a from the sheet. Through point P, a Gaussian cylinder is drawn with the cross-sectional area of A.

The following is the electric flux crossing through the Gaussian surface:

Φ = E x area of the circular caps of the cylinder

The electric lines of force and the curved surface of the cylinder are parallel to each other. Therefore, the flux due to the electric field of the plane sheet passes through the two circular caps of the cylinder.

Φ = E x 2A (eq.1)

From the Gauss theorem, we know that,

Φ = q/ε0

The charge enclosed by the Gaussian surface is given as,

q = 𝜎A

Therefore,

Φ = 𝜎A/ε0 (eq.2)

From eq.1 and eq.2,

E x 2A = 𝜎A/ε0

Therefore,

E = 𝜎/2ε0

The direction of an electric field will be in the outward direction when the charge density is positive and perpendicular to the infinite plane sheet.

The direction of an electric field will be in the inward direction when the charge density is negative and perpendicular to the infinite plane sheet.

Learn about the characteristics of electrical force with the help of this video:

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Frequently Asked Questions – FAQs

What will be the direction of the electric field intensity at a point due to a negative charge?

The direction of the electric field intensity at a point due to a negative charge will be radial and towards the charge.

What should be the size of the test charge used to measure the electric field at a point?

The size of the test charge used for measuring the electric field at a point should be infinitely small.

For a uniformly charged sphere, where will the electric field intensity be zero?

For a uniformly charged sphere, the electric field intensity will be zero at the centre.

What are the properties of an electric field?

The following are the properties of an electric field:

  • The electric field lines are perpendicular to the surface of the charge.
  • The electric field lines never intersect each other.
  • The number of electric field lines and the magnitude of the charge are directly proportional.

What is the unit of electric field?

The unit of electric field is volts per meter.

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