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

(1) Zero

(2) l²E

(3) 4l²E

(4) 6l²E

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface S is 

(1) $3q/{\epsilon }_0$

(2) $2q/{\epsilon }_0$

(3) $q/{\epsilon }_0$ 

(4) Zero

The electric flux for Gaussian surface A that enclose the charged particles in free space is (given q₁ = –14 nC, q₂ = 78.85 nC, q₃ = – 56 nC) 

(1) 10³ Nm² C^–1

(2) 10³ CN^-1 m^–2

(3) 6.32 × 10³ Nm² C^–1

(4) 6.32 × 10³ CN^-1 m^–2

The electric intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance r(r > R) from its axis is 

(1) Directly proportional to r²

(2) Directly proportional to r³

(3) Inversely proportional to r

(4) Inversely proportional to r²

A positively charged ball hangs from a silk thread. We put a positive test charge q₀ at a point and measure F/q₀, then it can be predicted that the electric field strength E 

(1) > F/q₀

(2) = F/q₀

(3) < F/q₀

(4) Cannot be estimated

The charge on 500 cc of water due to protons will be: 

An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is 

(1) ${\left(\frac{{\displaystyle pE}}{{\displaystyle I}}\right)}^{1/2}$

(2) ${\left(\frac{{\displaystyle pE}}{{\displaystyle I}}\right)}^{3/2}$

(3) ${\left(\frac{{\displaystyle I}}{{\displaystyle pE}}\right)}^{1/2}$

(4) ${\left(\frac{{\displaystyle p}}{{\displaystyle IE}}\right)}^{1/2}$

Two-point charges, +q and –q are held fixed at (–d, 0) and (d, 0) respectively of an (x, y) coordinate system. Then: 

The electric field due to a uniformly charged sphere of radius R as a function of the distance from its centre is represented graphically by 

(1)  (2)

(3)  (4)

Suppose the charge of a proton and an electron differ slightly. One of them is -e and the other is $\left(e+∆e\right)$. If the net of electrostatic force and gravitaional force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero,then $∆e$ is of the order [Given mass of hydrogen, $m_h$=1.67$\times {10}^{-27}$ kg]

(a) ${10}^{-20}C$

(b)${10}^{-23}C$

(c) ${10}^{-37}C$

(d) ${10}^{-47}C$