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Gauss Law Formula

Gauss’s Law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux in an area is defined as the electric field multiplied by the area of the surface projected in a plane and perpendicular to the field.

The electric field is the basic concept to know about electricity. Generally, the electric field of surface is calculated by applying coulomb’s law, but to calculate the electric field distribution in a closed surface, we need to understand the concept of Gauss law. It explains about the electric charge enclosed in a closed or the electric charge present in the enclosed closed surface.

The total charge enclosed in a closed surface is proportional to the total flux enclosed by the surface. If ϕ is total flux and ϵ0 is electric constant, the total electric charge Q enclosed by the surface is

Q = ϕ ϵ0

The Gauss law formula is expressed by

ϕ = Q / ϵ0

Where,

Q = total charge within the given surface,

ϵ0 = the electric constant.

Example 1

Find the total flux enclosed by the surface containing  three charges q1, q2, and q3 having charge 6 C, 5 C and 4 C

Solution:

Total charge,

Q = q1 + q2 + q3

   = 6 C + 5 C + 4 C

   = 15 C

The total flux is given by

ϕ = Q / ϵ0

ϕ = 15 C / 8.854×10−12

ϕ = 1.694 Nm2 / C−1

Therefore, ϕ =   1.694 Nm2 / C−1

Example 2

Calculate the electric flux in a cylinder of length 5 cm, radius 3 cm having electric field intensity 2 N/C.

Solution:

Given:

Length l is 5 cm,

Radius r is 3 cm,

Electric field intensity is given by

E = 2 N/C

Electric flux is given by

ϕ = E (2 ππ r l)

ϕ = 2 N/C (2 π × 0.03 m × 0.05 m)

ϕ = 0.0188 Nm2 / C−1

 

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