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.  $\frac{r}{3}\mathrm{from} q$

2.  $\frac{2r}{3}\mathrm{from} q$

3.  $2r \mathrm{from} q$

4.  $r \mathrm{from} 4q$

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

1.  Circular with equal radius

2.  Elliptical with the same major and minor axis

3.  Parabolic with the identical trajectory

4.  Hyperbolic with the identical trajectory

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.  $\frac{\rho r}{3 {\epsilon }_0}$

2.  $\frac{\rho R}{3 {\epsilon }_0}$

3.  $\frac{\rho r}{{\epsilon }_0}$

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

A short electric dipole having dipole moment $p\hat{i}$ is placed at origin and a point charge +q is placed at point (0, r). The force on dipole due to charge is in:

1.  +x-direction

2.  -x-direction

3.  +y-direction

4.  -y-direction