The electric potential V at any point x, y, z (all in meter) in space is given by V=4 x^2 volt.

Name: Problem 1633, Chapter 11: JEE Physics
Uploaded: 2021-10-02T14:43:23-08:00
Duration: 1 min 2 s
Channel: Narayan Hari
Description: The electric potential V at any point x, y, z (all in meter) in space is given by V=4 x^2 volt. The electric field at the point (1 m, 0,2 m) in Vm^-1 is (A)+8 i ∧(B) -8 i ∧(C) -16 i (D) +16 i

step 1 I can write the value of v is equal to 4x square here. The value of E is equal to minus dv by Dx

Question

The electric potential $\mathrm{V}$ at any point $\mathrm{x}, \mathrm{y}, \mathrm{z}$ (all in meter) 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 $\mathrm{Vm}^{-1}$ is $(\mathrm{A})+8 \mathrm{i} \wedge$ (B) $-8 \mathrm{i} \wedge$ (C) $-16 \mathrm{i}$ (D) $+16 \mathrm{i}$

   The electric potential $\mathrm{V}$ at any point $\mathrm{x}, \mathrm{y}, \mathrm{z}$ (all in meter) 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 $\mathrm{Vm}^{-1}$ is
$(\mathrm{A})+8 \mathrm{i} \wedge$
(B) $-8 \mathrm{i} \wedge$
(C) $-16 \mathrm{i}$
(D) $+16 \mathrm{i}$

JEE Physics

StemEZ 1st Edition

Chapter 11, Problem 1633

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Solved by Expert Narayan Hari

10/02/2021

Step 1

Step 1: The electric potential V is given by $V=4x^{2}$. Show more…

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The electric potential $\mathrm{V}$ at any point $\mathrm{x}, \mathrm{y}, \mathrm{z}$ (all in meter) 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 $\mathrm{Vm}^{-1}$ is $(\mathrm{A})+8 \mathrm{i} \wedge$ (B) $-8 \mathrm{i} \wedge$ (C) $-16 \mathrm{i}$ (D) $+16 \mathrm{i}$

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Key Concepts

Electric Field

The electric field is a vector field that describes the force experienced per unit charge at each point in space. It is directly related to the electric potential through the relationship E = -?V, meaning that the electric field points in the direction of the greatest decrease in the potential.

Gradient Operator

The gradient operator (?) is a mathematical tool used in vector calculus to measure the rate and direction of change in a scalar field. When applied to the electric potential, it reveals how the potential changes in space, thereby determining the direction and magnitude of the corresponding electric field.

Electric Potential

Electric potential is a scalar field that represents the electric potential energy per unit charge at various points in space. It helps determine the behavior of charges in an electric field and is measured in volts. Variations in the potential indicate how a charge would gain or lose energy as it moves through the field.

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