In a certain region of space, variation of potential with distance from origin as we move along $x$-axis is given by $V=8 x^2+2$, where $x$ is the $x$-coordinate of a point in space. The magnitude of electric field at a point $(-4,0)$ is .......... $V / m$
$-16$
$16$
$-64$
$64$
The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$ ?
$A, B$ and $C$ are three points in a uniform electric field. The electric potential is
A spherical charged conductor has surface charge density $\sigma $ . The electric field on its surface is $E$ and electric potential of conductor is $V$ . Now the radius of the sphere is halved keeping the charge to be constant. The new values of electric field and potential would be
A cathode ray tube contains a pair of parallel metal plates $1.0\, cm$ apart and $3.0\, cm$ long. A narrow horizontal beam of electron with a velocity $3 \times 10^7\, m/s$ passed down the tube midway between the plates. When a potential difference of $550\, V$ is maintained across the plates, it is found that the electron beam is so deflected that it just strikes the end of one of the plates. Then the specific charge of the electron in $C/kg$ is
$A B C$ is a right angled triangle situated in a uniform electric field $\vec{E}$ which is in the plane of the triangle. The points $A$ and $B$ are at the same potential of $15 \,V$ while the point $C$ is at a potential of $20 \,V . A B=3 \,cm$ and $B C=4 \,cm$. The magnitude of electric field is (in $S.I.$ Units)