A particle of mass 2 g and charge 1 $\mu C$ is held at a distance of 1 m from a fixed charge of 1 mC. If the particle is released then its speed, when it is at a distance of 10 m from the fixed charge, is

1.  55 m/s

2.  100 m/s

3.  45 m/s

4.  90 m/s

The insulation property of air breaks down at \(E = 3\times 10^{6}~\text{V/m}\). The maximum charge that can be given to a sphere of diameter \(5\) m is approximately:
1. \(2\times 10^{-5}~\text{C}\)
2. \(2\times 10^{-4}~\text{C}\)
3. \(2\times 10^{-3}~\text{C}\)
4. \(3\times 10^{-3}~\text{C}\)

Given below are two statements: 

Given below are two statements: 

Given below are two statements: 

The conducting shells A and B are arranged as shown below. If the charge on the shell B is q then electric flux linked with the spherical Gaussian surface S is

1.  $\frac{q}{{\epsilon }_0}$

2.  $-\frac{q}{2{\epsilon }_0}$

3.  $-\frac{q}{{\epsilon }_0}$

4.  $\frac{q}{2{\epsilon }_0}$

Which of the following is incorrect about the electrostatic field lines?

1.  These can be never be closed curves

2.  On a conducting surface, the lines are perpendicular

3.  They can pass through a conductor

4.  If the lines are equispaced and parallel to one another, then the field is uniform

Some equipotential surfaces are shown in the figure. The electric field at points \(A\), \(B\) and \(C\) are respectively:

An electric field is given by \(\vec E=(\hat i+2\hat j+\hat k)\) N/C. The work done in moving a \(1\) C charge from \(\vec {r_A}=(2\hat i+2\hat j)\) m to \(\vec {r_B}=(4\hat i+\hat j)\) m is:
1. \(8\) J
2. \(4\) J
3. \(-4\) J
4. zero

If n identical drops, each of capacitance C, coalesce to form a single big drop, the capacitance of the big drop will be

1. $n^{3}C$

2. nC 

3. $n^{1/2}C$

4. $n^{1/3}C$