Side length of equilateral triangle is $d. P$ is mid of side then potential at point $P, V_P$ is
$\frac{Q}{{2\pi { \in _0}d}}\left[ {2 + \sqrt 3 } \right]$
$\frac{Q}{{2\pi { \in _0}d}}\left[ {2 + \frac{1}{{\sqrt 3 }}} \right]$
$\frac{Q}{{4\pi { \in _0}d}}\left[ {4 + \sqrt 3 } \right]$
Zero
Two opposite and equal charges $4 \times {10^{ - 8}}\, coulomb$ when placed $2 \times {10^{ - 2}}\,cm$ away, form a dipole. If this dipole is placed in an external electric field $4 \times 10^8\, newton / coulomb$ , the value of maximum torque and the work done in rotating it through $180^o$ will be
In the circuit shown, a potential difference of $60\,V$ is applied across $AB$. The potential difference between the point $M$ and $N$ is.....$V$
The potential $V$ is varying with $x$ and $y$ as $V = \frac{1}{2}({y^2} - 4x)\,volts$ The field at $(1\,m,\,1\,m)$ is
Two capacitor one of capacitance $C$ and other capacitance $C/2$ are connected with a battery of $V$ $volt$ then heat produced in connecting wire
Two spherical conductors $A$ and $B$ of radii $1\, mm$ and $2\, mm$ are separated by a distance of $5\, cm$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is-