The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of 100 volt is 

(1) 1

(2) $\sqrt{\frac{2m_e}{m_{\alpha }}}$

(3) $\sqrt{\frac{m_e}{m_{\alpha }}}$

(4) $\sqrt{\frac{m_e}{2m_{\alpha }}}$

When a proton is accelerated through 1V, then its kinetic energy will be -

(1) 1840 eV

(2) 13.6 eV

(3) 1 eV

(4) 0.54 eV

Ten electrons are equally spaced and fixed around a circle of radius R. Relative to V = 0 at infinity, the electrostatic potential V and the electric field E at the centre C are:

The displacement of a charge Q in the electric field $E=e_1\hat{i}+e_2\hat{j}+e_3\hat{k}$ is $\hat{r}=a\hat{i}+b\hat{j}$. The work done is 

(1) $Q(a{e}_1+b{e}_2)$

(2) $Q\sqrt{{\left(a{e}_1\right)}^2+{\left(b{e}_2\right)}^2}$

(3) $Q(e_1+e_2)\sqrt{a^2+b^2}$

(4) $Q\left(\sqrt{e_1^2+e_2^2)}\right(a+b)$

Three charges Q, +q and +q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

(1) $\frac{-q}{1+\sqrt{2}}$

(2) $\frac{-2q}{2+\sqrt{2}}$

(3) –2q

(4) +q

A cube of a metal is given a positive charge Q. For the above system, which of the following statements is true?

Three charges \(Q\), \(+q \) and \(+q \) are placed at the vertices of an equilateral triangle of side \(l\) as shown in the figure. If the net electrostatic energy of the system is zero, then \(Q\) is equal to:

Electric potential at any point is $V=-5x+3y+\sqrt{15}z$, then the magnitude of the electric field is

(1) $3\sqrt{2}$

(2) $4\sqrt{2}$

(3) $5\sqrt{2}$

(4) 7

Kinetic energy of an electron accelerated in a potential difference of 100 V is 

(1) 1.6 × 10^–17 J

(2) 1.6 × 10²¹ J

(3) 1.6 × 10^–29 J

(4) 1.6 × 10^–34 J

If identical charges (–q) are placed at each corner of a cube of side b, then electric potential energy of charge (+q) which is placed at centre of the cube will be -

(1) $\frac{8\sqrt{2}{q}^2}{4\pi {\epsilon }_{0}b}$

(2) $\frac{-8\sqrt{2}{q}^2}{\pi {\epsilon }_{0}b}$

(3) $\frac{-4\sqrt{2}{q}^2}{\pi {\epsilon }_{0}b}$

(4) $\frac{-4q^2}{\sqrt{3}\pi {\epsilon }_{0}b}$