## Gauss Theorem

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# Gauss’s Theorem

If a point charge of + Q coulombs is considered to be placed at the centre of a sphere of radius r metres, as shown in the electric flux emanated from the charge Q is Q coulombs and is normal to the surface of the sphere.

Now if a point charge of + Q coulombs is considered placed at any point (other than centre 0) as shown in the electric flux or lines of force emanated from this charge is Q but not normal to the surface. This flux can however be resolved along the normal to the surface known as cos Θ components and another along the perpendicular to the normal to the surface known as sin Θ components. If all the sin Θ components of the flux all the surface are added, their resultant is zero while the sum of all cos Θ components of lines or force all over the surface is equal to Q.

Thus the total flux traversing a surface completely surrounding the charge of Q coulombs is Q. This is known as Gauss’s theorem.

If there are number of charges Q

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Now if a point charge of + Q coulombs is considered placed at any point (other than centre 0) as shown in the electric flux or lines of force emanated from this charge is Q but not normal to the surface. This flux can however be resolved along the normal to the surface known as cos Θ components and another along the perpendicular to the normal to the surface known as sin Θ components. If all the sin Θ components of the flux all the surface are added, their resultant is zero while the sum of all cos Θ components of lines or force all over the surface is equal to Q.

Thus the total flux traversing a surface completely surrounding the charge of Q coulombs is Q. This is known as Gauss’s theorem.

If there are number of charges Q

_{1},Q_{2}-Q_{3},Q_{4}etc. enclosed by the surface, as shown in ( ) then according to Gauss’s theorem the total flux crossing the surface is given as Ψ = Q_{1}+Q_{2}-Q_{3}+Q_{4}+........For more help in

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