A point charge q is placed over a horizontal square of side L at a normal distance of L/4 from its centre. Electric flux through the square is

1. $\mathrm{\varphi }=\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_{0}}$

2. $\mathrm{\varphi }<\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_{0}}$

3. $\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_{0}}<\mathrm{\varphi }<\frac{\mathrm{q}}{{\mathrm{\epsilon }}_{0}}$

4. $\mathrm{\varphi }>\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_{0}}$

Concept Questions :-

Gauss law
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A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge –Q. The surface charge density on the inner and outer surfaces of the spherical shell will be

(1) $-\frac{2Q}{4\pi {b}^{2}},\frac{Q}{4\pi {c}^{2}}$

(2) $-\frac{Q}{4\pi {b}^{2}},\frac{Q}{4\pi {c}^{2}}$

(3) $0,\frac{Q}{4\pi {c}^{2}}$

(4) None of the above

Concept Questions :-

Gauss law
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A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

(1) $2\pi {R}^{2}E$

(2) $\pi {R}^{2}/E$

(3) $\left(\pi {R}^{2}-\pi R\right)/E$

(4) Zero

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Gauss law
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An electric charge is placed at the centre of a cube of side α. The electric flux on one of its faces will be

(1) $\frac{q}{6{\epsilon }_{0}}$

(2) $\frac{q}{{\epsilon }_{0}{a}^{2}}$

(3) $\frac{q}{4\pi {\epsilon }_{0}{a}^{2}}$

(4) $\frac{q}{{\epsilon }_{0}}$

Concept Questions :-

Gauss law
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Total electric flux coming out of a unit positive charge put in air is

(1) ${\epsilon }_{0}$

(2) ${\epsilon }_{0}^{-1}$

(3) ${\left(4p{\epsilon }_{0}\right)}^{-1}$

(4) $4\pi {\epsilon }_{0}$

Concept Questions :-

Gauss law
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A cube of side l is placed in a uniform field E, where $E=E\stackrel{^}{i}$. The net electric flux through the cube is

(1) Zero

(2) l2E

(3) 4l2E

(4) 6l2E

Concept Questions :-

Gauss law
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A charge q is placed at the centre of the open end of the cylindrical vessel. The flux of the electric field through the surface of the vessel is

(1) Zero

(2) $\frac{q}{{\epsilon }_{0}}$

(3) $\frac{q}{2{\epsilon }_{0}}$

(4) $\frac{2q}{{\epsilon }_{0}}$

Concept Questions :-

Gauss law
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According to Gauss’ Theorem, electric field of an infinitely long straight wire is proportional to

(1) r

(2) $\frac{1}{{r}^{2}}$

(3) $\frac{1}{{r}^{3}}$

(4) $\frac{1}{r}$

Concept Questions :-

Gauss law
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Electric charge is uniformly distributed along a long straight wire of radius 1mm. The charge per cm length of the wire is Q coulomb. Another cylindrical surface of radius 50 cm and length 1m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is

(1) $\frac{Q}{{\epsilon }_{0}}$

(2) $\frac{100Q}{{\epsilon }_{0}}$

(3) $\frac{10Q}{\left(\pi {\epsilon }_{0}\right)}$

(4) $\frac{100Q}{\left(\pi {\epsilon }_{0}\right)}$

Concept Questions :-

Gauss law
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The S.I. unit of electric flux is

(1) Weber

(2) Newton per coulomb

(3) Volt × metre

(4) Joule per coulomb

Concept Questions :-

Gauss law