Three infinitely long charge sheets are placed as shown in the figure. The electric field at point P is 

(1) $\frac{2\sigma }{{\epsilon }_o}\hat{k}$

(2) $-\frac{2\sigma }{{\epsilon }_o}\hat{k}$

(3) $\frac{4\sigma }{{\epsilon }_o}\hat{k}$

(4) $-\frac{4\sigma }{{\epsilon }_o}\hat{k}$

Two infinitely long parallel conducting plates having surface charge densities +σ and –σ respectively, are separated by a small distance. The medium between the plates is a vacuum. If ε₀ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is 

(1)  $0 volts/meter$

(2) $\frac{\sigma }{2{\epsilon }_o}volts/meter$

(3) $\frac{\sigma }{{\epsilon }_o}volts/meter$

(4) $\frac{2\sigma }{{\epsilon }_o}volts/meter$ 

Four-point +ve charges of the same magnitude (Q) are placed at four corners of a rigid square frame as shown in the figure. The plane of the frame is perpendicular to Z-axis. If a –ve point charge is placed at a distance z away from the above frame (z<<L) then 

1. – ve charge oscillates along the Z-axis.

2. It moves away from the frame.

3. It moves slowly towards the frame and stays in the plane of the frame.

4. It passes through the frame only once.

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) $(\pi R^2-\pi R)/E$ 

(4) Zero

Electric field at a point varies as r⁰ for

(1) An electric dipole

(2) A point charge

(3) A plane infinite sheet of charge

(4) A line charge of infinite length

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) $4\pi {\epsilon }_0$ 

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

Eight dipoles of charges of magnitude \((e)\) are placed inside a cube. The total electric flux coming out of the cube will be: 
1. \(\frac{8e}{\epsilon _{0}}\)
2. \(\frac{16e}{\epsilon _{0}}\)
3. \(\frac{e}{\epsilon _{0}}\)
4. zero

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) $\frac{2q}{{\epsilon }_0}$ 

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

      
1. \(\frac{Q}{\varepsilon _{0}}\)

2. \(\frac{100Q}{\varepsilon _{0}}\)

3. \(\frac{10Q}{\pi\varepsilon _{0}}\)

4. \(\frac{100Q}{\pi\varepsilon _{0}}\)