Relation between Field and Potential

The potential at a point $x$ due to some charge is given by equation $V\left(x\right)=\frac{20}{(x^2-4)}$ volts. Then electric field at $x=4$ is given by

The electric potential function for some electric field is defined by $V=-5x+3y+\sqrt{15}z$. The intensity of electric field (in SI unit) at point $(x, y, z)$ is

The maximum electric field that can be held in air without producing ionisation of air is $107 \mathrm{V} {\mathrm{m}}^{-1}$. The maximum potential therefore, to which a conducting sphere of radius $0.10 \mathrm{m}$ can be charged in air, is :

Electric field at a distance $x$ from the origin is given as $E=\frac{100 \mathrm{N}-{\mathrm{m}}^2 {\mathrm{C}}^{-1}}{x^2}.$ Then potential difference between the points situated at $x=10 \mathrm{m}$ and $x=20 \mathrm{m}$ is :-

In the following graph, the magnitude of maximum electric field is :-

A positively charged particle is released from rest in an uniform electric field. The electric potential energy of the charge

What is angle between electric field and equipotential surface?

The electric potential at a point $(\mathrm{x}, \mathrm{y}, \mathrm{z})$ (all in meters) in free space is given by $\mathrm{V}=2{\mathrm{x}}^2$ Volts. Determine electric field intensity at point  $(1 \mathrm{m},2 \mathrm{m},3 \mathrm{m})$ in terms of $\hat{\mathrm{i}} \mathrm{V}/\mathrm{m}$.

For some electric field, potential at a point $(\mathrm{x}, \mathrm{y})$ is given as $\mathrm{Y}=6\mathrm{xy}+{\mathrm{y}}^2-{\mathrm{x}}^2$. Determine the electric field at this point.

Derive relation between electric potential and field.

The electric potential in complete volume of a charged conductor is same as that on its surface. Why?

If potential function is $\mathrm{V}=4\mathrm{x}+3\mathrm{y}$ volts, then calculate magnitude of electric field intensity at point $\left(2,1\right)$ meter.

The electric potential function for some electric field is defined by $\mathrm{V}=-5\mathrm{x}+3\mathrm{y}+\sqrt{15}\mathrm{z}$. The intensity of electric field $(\mathrm{in} \mathrm{S}.\mathrm{I}. \mathrm{units})$ at point $(\mathrm{x}, \mathrm{y}, \mathrm{z})$ is

In some regions where electric field intensity $E$ is zero, the electric potential varies with distance according to

An electron at rest is accelerated through a potential difference of $200 \mathrm{V}.$ If the electron acquires a velocity of $8.4\times {10}^{\mathrm{8 }}\mathrm{c}\mathrm{m}/\mathrm{s},$ its $\frac{e}{m}$ ratio is

A uniform electric field is prevailing in $X$ -direction in certain region. The co-ordinates of points P, Q and R are (0, 0), (2, 0) and (0, 2) respectively. Which of the following alternatives is true for the potentials at these points?

Electric field in a region is given by $E=\left(\frac{M}{x^3}\right)\widehat{i}$ , then the correct expression for the potential in the region is (assume potential at infinity is zero).

From a point charge, there is a fixed point A. At A, there is an electric field of $500 V/m$ and potential difference of 3000V. Distance between point charge and A will be

Find the surface density of electric charge at a place on the earth's surface where the rate of fall of potential is 2.5 V

Two concentric conducting spheres of radii $r_1$ and $r_2\left(r_1<r_2\right)$ carry electric charges of $+Q \& -Q$ respectively. The region between the sphere is filled with two insulating layers of dielectric constant ${\epsilon }_1$ and ${\epsilon }_2$ and width $d_1$ and $d_2$ respectively. Variation of potential and electric field with radial distance from $O$ is given. Select the correct one. (assume $V$ at $r_2=0$ )