The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of $100\, volts$ is
$1$
$\sqrt {\frac{{2{m_e}}}{{{m_\alpha }}}} $
$\sqrt {\frac{{{m_e}}}{{{m_\alpha }}}} $
$\sqrt {\frac{{{m_e}}}{{2{m_\alpha }}}} $
Two charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively.
$(a)$ What is the electrostatic potential at the points $(0,0, z)$ and $(x, y, 0) ?$
$(b)$ Obtain the dependence of potential on the distance $r$ of a point from the origin when $r / a\,>\,>\,1$
$(c)$ How much work is done in moving a small test charge from the point $(5,0,0)$ to $(-7,0,0)$ along the $x$ -axis? Does the answer change if the path of the test charge between the same points is not along the $x$ -axis?
If an $\alpha$-particle and a proton are accelerated from rest by a potential difference of 1 megavolt then the ratio of their kinetic energy will be
Two electrons are moving towards each other, each with a velocity of $10^6 \,m / s$. What will be closest distance of approach between them is ......... $m$
Which of the following statement$(s)$ is/are correct?
$(A)$ If the electric field due to a point charge varies as $r^{-25}$ instead of $r^{-2}$, then the Gauss law will still be valid.
$(B)$ The Gauss law can be used to calculate the field distribution around an electric dipole.
$(C)$ If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.
$(D)$ The work done by the external force in moving a unit positive charge from point $A$ at potential $V_A$ to point $B$ at potential $V_B$ is $\left(V_B-V_A\right)$.
There exists a uniform electric field $E=4 \times 10^5 \,Vm ^{-1}$ directed along negative $x$-axis such that electric potential at origin is zero. Acharge of $-200 \,\mu C$ is placed at origin, and a charge of $+200 \,\mu C$ is placed at $(3 \,m , 0)$. The electrostatic potential energy of the system is ...........$J$