Use Gauss' law to derive the expression for the electric field ( E → ) due to a straight uniformly charged infinite line of charge density λ C m .

Consider a thin infinitely long straight wire having a uniform linear charge density λ C m − 1 . By symmetry the field its magnitude is same at all points equidistant from the line charge. Selecting a cylindrical Gaussian surface of radius r , length l and with its axis along the line charge, As show in the figure, Net flux can be written as ϕ E = ∮ S E → ⋅ d S → = ∫ S 1 d S → 1 + ∫ S 2 E → ⋅ d S → 1 + ∫ S 3 E → ⋅ d S → 3 = ∫ S 1 E d S 1 cos 0 ∘ + ∫ S 2 E d S 2 cos 90 ∘ + ∫ S 3 E d S 3 cos 90 ∘ = E ∫ d S 1 + 0 + 0 = E × area of the curved surface or ϕ E = E × 2 π r l Charge enclosed by the Gaussian surface, q = λ l Using Gauss’ theorem, ϕ E = q ε 0 ⇒ E . 2 π r l = λ l ε 0 ⇒ E = λ 2 π ε 0 r Vectorial, E → = λ 2 π ε 0 r n ^ .

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12th CBSE

IMPORTANT

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Using Gauss's law, deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius $R$ at a point inside the shell.

Plot a graph showing variation of electric field as a function of $r > R$ and $r < R$ ( $r$ being the distance from the centre of the shell).

Important Questions on Electric Charges and Field

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Text Based Exercises>Q 11

State Gauss's law in electrostatics. Using this theorem, show mathematically that for any point outside the shell, the field due to uniformly charged thin spherical shell is the same as if entire charge of the shell is concentrated at the centre. Why do you expect the electric field inside the shell to be zero according to this theorem?

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Text Based Exercises>Q 11

Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative.

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Text Based Exercises>Q 12

State the theorem which relates total charge enclosed within a closed surface and the electric flux passing through it. Prove it for a single point charge.

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Text Based Exercises>Q 12

An 'atom' was earlier assumed to be a sphere of radius a having a positively charged point nucleus of charge

+ Z e

at its centre. This nucleus was believed to be surrounded by a uniform density of negative charge that made the atom neutral as a whole. Use this theorem to find the electric field of this 'atom' at a distance

r (r < a)

from the centre of the atom.

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Text Based Exercises>Q 13

Define electric flux quantity?

A point charge $q$ is at a distance of $\frac{d}{2}$ directly above the centre of a square of side $d$ , as shown in Fig. 1.163. Use Gauss' law to obtain the expression for the electric flux through the square.

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Text Based Exercises>Q 13

If the point charge is now moved to a distance ‘ $d$ ’ from the centre of the square and the side of the square is doubled, explain how the electric flux will be affected.

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Text Based Exercises>Q 14

Use Gauss' law to derive the expression for the electric field

(\vec{E})

due to a straight
uniformly charged infinite line of charge density

\frac{λ C}{m}

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Text Based Exercises>Q 14

Draw a graph to show the variation of

E

with perpendicular distance

r

from the line of charge.

Using Gauss's law, deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point inside the shell. Plot a graph showing variation of electric field as a function of r>R and r<R(r being the distance from the centre of the shell).

Important Questions on Electric Charges and Field

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