A long thin rod is charged such that charge per unit length of the rod is $\lambda$. The rod is inserted into a hollow spherical surface of radius R. Maximum electric flux coming out the surface is

1.  $\frac{\lambda R}{{\epsilon }_0}$

2.  $\frac{2\lambda \pi R^2}{{\epsilon }_0}$

3.  $\frac{2\lambda R}{{\epsilon }_0}$

4.  $\frac{2\lambda R^2}{{\epsilon }_0}$

Two charges q and 4q are separated by a distance r. The neutral point(in between the line joining the charges) is at a distance:

1.  $\frac{r}{3}\mathrm{from}<mspace\; width="1em"></mspace>q$

2.  $\frac{2r}{3}\mathrm{from}<mspace\; width="1em"></mspace>q$

3.  $2r<mspace\; width="1em"></mspace>\mathrm{from}<mspace\; width="1em"></mspace>q$

4.  $r<mspace\; width="1em"></mspace>\mathrm{from}<mspace\; width="1em"></mspace>4q$

A positron and a proton are projected normally into a uniform electric field with equal kinetic energy. The trajectory followed by them are:

The distance between two point charges is increased by 10%. The force of interaction

1.  Increases by 10%

2.  Decreases by 10%

3.  Decreases by 17%

4.  Increases by 17%

Cm is the SI unit of 

1.  Electric flux

2.  Electric potential

3.  Electric dipole moment

4.  Electric field intensity

A solid sphere of radius R has a uniform distribution of electric charge in its volume. At a distance x from its center (x<R), the electric field is directly proportional to

1.  $\frac{1}{x^2}$

2.  $\frac{1}{x}$

3.  x

4.  $x^2$

An insulated sphere of radius R has a uniform charge density $\rho$. The electric field at a distance r from the center of the sphere (r<R) is-

1.  $\frac{\rho <mspace\; width="1em"></mspace>r}{3<mspace\; width="1em"></mspace>{\epsilon }_0}$

2.  $\frac{\rho <mspace\; width="1em"></mspace>R}{3<mspace\; width="1em"></mspace>{\epsilon }_0}$

3.  $\frac{\rho <mspace\; width="1em"></mspace>r}{{\epsilon }_0}$

4.  $\frac{\rho }{{\epsilon }_0}R$

The electric flux from a cube of edge \(l\) is \(\phi\). What will be its value if the edge of the cube is made \(2l\) and the charge enclosed is halved?
1. \(\frac{1}{2}\phi\)
2. \(2\phi\)
3. \(4\phi\)
4. \(\phi\)

Three identical plates are kept as shown. Plate 1 is given -5Q charge and plate 3 is given Q charge. Electric field intensity at point x is

1.  $\frac{3Q}{A{\epsilon }_0}down$

2.  $\frac{3Q}{2A{\epsilon }_0}down$

3.  $\frac{3Q}{2A{\epsilon }_0}upward$

4.  $\frac{3Q}{A{\epsilon }_0}upward$

The equation of trajectory of a charged particle moving in xy plane in a uniform electric field maybe 

1.  y = 2x + 8

2.  x = $y^2$ + 4

3.  y = 2$x^2$ + 6

4.  All of these