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Gauss's Law

Charge Q1 a...

Question

Charge $Q_{1}$ and $Q_{2}$ lie inside and outside respectively of a closed surface S. Let E be the field at any point on S and $ϕ$ be the flux of E over S.

A

If

Q_{1}

changes, both E and

ϕ

will change

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B

If

Q_{2}

changes, E will change but

ϕ

will not change

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C

If

Q_{1}

= 0 and

Q_{2} \neq

0 then E

\neq

0 but

ϕ

= 0

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D

If

Q_{1} \neq

0 and

Q_{2}

= 0 then E = 0 but

ϕ \neq

0

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Solution

The correct options are
A If $Q_{1}$ changes, both E and $ϕ$ will change
B If $Q_{2}$ changes, E will change but $ϕ$ will not change
D If $Q_{1}$ = 0 and $Q_{2} \neq$ 0 then E $\neq$ 0 but $ϕ$ = 0
As the electric field at any point on surface S is the resultant effect due to all charges in the system, so field at any point on S is $E = E_{1} + E_{2}$ where $E_{1}$ is the field due to $Q_{1}$ and $E_{2}$ is the field due to $Q_{2}$
Applying Gauss's law, the flux over S , $ϕ = \frac{Q_{e n}}{ϵ_{0}}$ where $Q_{e n} = Q_{1} =$ charge enclosed by S.
Thus field depends on both charges but flux is only depends on the charges $Q_{1}$ .
So according to this the options A,B and C will be correct.

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Similar questions

Q_{1}

Q_{2}

lie inside and outside respectively of a closed surface

S

E

be the field at any point on

S

ϕ

E

(electric field) over

S

	List-I		List-II
(P)	If $Q_{1} = 0$ and $Q_{2} \neq 0$ then	(1)	Both $E$ and $ϕ$ will change
(Q)	If $Q_{1} \neq 0$ and $Q_{2} = 0$ then	(2)	$E \neq 0$ and $ϕ \neq 0$
(R)	If $Q_{2}$ changes	(3)	net electric field will change but $ϕ$ will not change
(S)	If $Q_{1}$ changes	(4)	$E \neq 0$ but $ϕ = 0$

Q_{1}

Q_{2}

lie inside and outside respectively of a closed surface S. Let E be the field at any point on S and

ϕ

be the flux of E over S

Q_{1}

Q_{2}

lie inside and outside respectively of a closed surface S. Let E be the field at any point on S and

ψ

be the flux of E over S.

θ_{1}

θ_{2}

lie inside and out side respectively for a closed surface s. Let E be the field at a point on S and

ϕ

be flux of E over S

Q. A conducting shell of inner radius

R_{1}

and outer radius

R_{2}

is given a charge

+ Q

. A point charge

q_{1}

is placed inside the shell and

q_{2}

is placed outside the shell.

Then for various locations of

q_{1}

q_{2}

, match the following entries of column

- I

with the entries of column

- II

Column- $I$	Column- $II$
$(i) .$ If $q_{1}$ is at center and $q_{2} = 0$ , then $\to E$ at center of shell due to charge on outer surface of shell is	$(a) . \frac{q_{1}}{4 π ε_{0} r^{2}}$
$(ii) .$ If $q_{1}$ is at center and $q_{2}$ is at distance $r$ from the center, then $\to E$ at a point distant $r_{2}$ ( $> r$ ) from the center of the shell due to outer surface charge is	$(b) .$ Zero
$(iii) .$ If $q_{1}$ is not at center and $q_{2} = 0$ , then $\to E$ at point $P$ ( $P$ is at distance $r$ from $q_{1}$ due to charge of the inner surface of shell) is	$(c) .$ Cant be determined

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