The figure shows the electric lines of force emerging from a charged body. If the electric field at \(A\) and \(B\) are \(E_A\) and \(E_B\) respectively and if the displacement between \(A\) and \(B\) is \(r,\) then:

1. \(E_A>E_B\)

2. \(E_A<E_B\)

3. $E_A=\frac{E_B}{r}$

4. $E_A=\frac{E_B}{r^2}$

A thin conducting ring of radius \(R\) is given a charge \(+Q.\) The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E.\) The electric field at the centre due to the charge on the part \(ACDB\) of the ring is:

               

A charged particle q of mass m is released on the \(y\text-\)axis at \(y=a\) in an electric field \(\vec E = -4y \hat{j}.\) The speed of particle on reaching the origin will be:
1. \(\sqrt{\frac{2 a}{m q}}\)
2. \(\frac{a}{\sqrt{m q}}\)
3. \(2 a \sqrt{\frac{q}{m}}\)
4. \(2 \sqrt{\frac{a}{m q}}\)

Three identical positive point charges, as shown are placed at the vertices of an isosceles right-angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point \(M\) of the hypotenuse?
                 
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

A charge \(q\) is placed in a uniform electric field \(E.\) If it is released, then the kinetic energy of the charge after travelling distance \(y\) will be:

The electrostatic field due to a charged conductor just outside the conductor is:

Two-point charges \(+8q\) and \(-2q\) are located at \(x=0\) and \(x=L\) respectively. The location of a point on the \(x\text-\)axis at which the net electric field due to these two point charges is zero is:
1. \(8L\)
2. \(4L\)
3. \(2L\)
4. \(\frac{L}{4}\)

A spherical conductor of radius \(10~\text{cm}\) has a charge of \(3.2 \times 10^{-7}~\text{C}\) distributed uniformly. What is the magnitude of the electric field at a point \(15~\text{cm}\) from the center of the sphere? 
\(\dfrac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\)
1. \(1.28\times 10^{5}~\text{N/C}\)
2. \(1.28\times 10^{6}~\text{N/C}\)
3. \(1.28\times 10^{7}~\text{N/C}\)
4. \(1.28\times 10^{4}~\text{N/C}\)

A toy car with charge \(q\) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec E.\)Due to the force \(q\vec E,\) its velocity increases from \(0\) to \(6~\text{m/s}\) in a one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between \(0\) to \(3\) seconds are respectively:
1. \(2~\text{m/s}, ~4~\text{m/s}\)
2. \(1~\text{m/s}, ~3~\text{m/s}\)
3. \(1~\text{m/s}, ~3.5~\text{m/s}\)
4. \(1.5~\text{m/s},~ 3~\text{m/s}\)

A charged ball \(B\) hangs from a silk thread \(S,\) which makes an angle \(\theta\) with a large charged conducting sheet \(P,\) as shown in the figure. The surface charge density \(\sigma\) of the sheet is proportional to: 

1. \(\sin\theta\)

2. \(\tan\theta\)

3. \(\cos\theta\)

4. \(\cot\theta\)