The electric Potential V at any Point 0(x, y, z all in meters ) in space is given by V=4 x^2 vol

step 1 I have given potential at a point is 4 x square volt. We have to find the electric field at 1 me

The electric Potential V at any Point 0(x, y, z all in...

The electric Potential $\mathrm{V}$ at any Point $0(\mathrm{x}, \mathrm{y}, \mathrm{z}$ all in meters $)$ in space is given by $\mathrm{V}=4 \mathrm{x}^{2}$ volt. The electric field at the point $(1 \mathrm{~m}, 0.2 \mathrm{~m})$ in volt meter is $\ldots \ldots .$ (A) 8 , along negative $\mathrm{x}$ - axis (B) 8 , along positives $\mathrm{x}$ - axis (C) 16 , along negative $\mathrm{x}$ -axis (D) 16 , along positives $\mathrm{x}$ -axis

The electric Potential $\mathrm{V}$ at any Point $0(\mathrm{x}, \mathrm{y}, \mathrm{z}$ all in meters $)$ in space is given by $\mathrm{V}=4 \mathrm{x}^{2}$ volt. The electric field at the point $(1 \mathrm{~m}, 0.2 \mathrm{~m})$ in volt meter is $\ldots \ldots .$
(A) 8 , along negative $\mathrm{x}$ - axis
(B) 8 , along positives $\mathrm{x}$ - axis
(C) 16 , along negative $\mathrm{x}$ -axis
(D) 16 , along positives $\mathrm{x}$ -axis

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Key Concepts

Relationship between Electric Potential and Electric Field

The electric field is directly related to the spatial variation of the electric potential through the equation E = -?V. This formulation shows that the electric field points in the direction of the steepest decrease in potential, linking energy considerations with force directions in electrostatics.

Gradient Operator

The gradient operator is a vector differential operator that indicates the direction and rate of fastest increase of a scalar field. In terms of electric potential, the negative gradient gives the electric field, which reflects how the potential changes in space and where charges would move naturally.

Electric Potential

Electric potential is a scalar quantity that represents the energy per unit charge at a point in space, typically expressed as a function of spatial coordinates. It provides a measure of the work done in bringing a unit charge from infinity to that point in the presence of an electric field.

Electric Field

The electric field is a vector quantity that denotes the force experienced by a unit positive charge placed in a region of space. It is derived from the electric potential and indicates both the magnitude and the direction of the force acting on charges.

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