Electromagnetism- Electric Field

Electric Field

The clods integral of electric field intensity is equal to q/ε0 where q is charge enclosed in the closed surface. In other words total electric flux through a closed surface enclosing a charge q is given by§E.dS = q/ε₀

If W is at right angle to the surface area A at all points and has the same magnitude at all points of the surface then E₁= E and ∫E₁d_A= E_A.

If E is parallel to the surface on all points thenE₁= 0hence integral is also zero.

IfE = 0hence integral is also zero.

IfE = 0at all points on a surface then∅= 0.

The surface need not be a real physical surface; it can be a hypothetical one.

Electric field in?E. dSis complete electric field. It may be partly far to charge within the surface and partly due to charge courtside the surface. However, if there is no charge enclosed in the Gaussian surfaceE₁will be zero and hence?E dS = 0.

While evaluating?E, dS, the field should lie on the surface and there should be enough symmetry to evaluate the integral.

Electric field due to a long threads (Line charge) having linear charge densityλis

E = λ/2πε₀y = 18 x 10⁹λ/y

Electric field due to a uniformly charged sphere of radius R having charge Q

E_inside= Qx/4πε₀R³x < R

E_surface= Q/4πε₀R x = R

E_outside= Q/4πε₀x²x > R

Potential due to a uniformly charged sphere

V_inside= Q/4πε₀R + ∫xR - Qx/4πε₀R³dx x < R

V_surface= Q/4πε₀R x = R

V_outside= Q/4πε₀R x > R

Electric filed doer to a thin plane sheet (long) of charge densityσ

E = σ/2ε₀

Electric field due to a charged surface having surface charge densityσ

E = σ/ε₀

Electric field due to a conducting plate:-E = σ/2ε₀

Electric field due to a non-conducting plate:-E = σ/ε0

Electric field between two oppositely charged sheets at any point isE_in= σ/ε₀= (E₁+ E2)assuming equal surface charge density, for example, in a capacitor. Electric field intensity is zero at any point outside the plates asE_net= E₁- E₂= 0.

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