The amount of work done in moving a charge from one point to another along an equipotential line or surface charge isa)Zerob)Infinityc)Oned)TwoCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

W = Q*∆V .              As potential is same in equipotential line ∆V = 0.        therefore W= 0.

Answer

This is because of the potential difference between any two points of equipotential surface is zero . therefore no work done on a charge from one point to another .

Answer

(A)

Answer

If VA=VB on equipotential surface then w=q(VB-VA) equals to 0

Answer

Because electric field is perpendicular to the path at all  point along the path

Answer

Equipotential Lines and Surfaces
Equipotential lines and surfaces are imaginary lines or surfaces in an electric field that connect points or areas with the same electric potential. These lines or surfaces are always perpendicular to the electric field lines, and they help us visualize the distribution of electric potential in a given region.

Work Done in Moving a Charge along an Equipotential Line
When a charge is moved along an equipotential line, no work is done on the charge. This is because the electric field is perpendicular to the equipotential lines, and work is only done when a force is applied in the direction of displacement. Since the electric field is perpendicular to the equipotential lines, there is no component of the electric field force in the direction of displacement, and therefore no work is done.

Explanation of the Correct Answer
The correct answer is option 'A' - Zero. This means that the amount of work done in moving a charge from one point to another along an equipotential line or surface is zero. This is because the electric field is always perpendicular to the equipotential lines or surfaces.

Reason for Zero Work
The work done in moving a charge is given by the equation:
Work = Force × Distance × cos(θ)
Where:
- Force is the component of the electric field force in the direction of displacement,
- Distance is the displacement between the initial and final points, and
- θ is the angle between the force and displacement vectors.

In the case of moving a charge along an equipotential line or surface, the angle θ between the force and displacement vectors is 90 degrees, as the electric field is perpendicular to the equipotential lines. Therefore, the cosine of 90 degrees is zero, and the work done is zero.

Significance of Zero Work
The fact that no work is done in moving a charge along an equipotential line or surface is significant because it tells us that the electric potential remains constant along these lines or surfaces. This means that the work done in moving a charge between any two points along an equipotential line is independent of the path taken.

Conclusion
In summary, the amount of work done in moving a charge from one point to another along an equipotential line or surface is zero. This is because the electric field is perpendicular to the equipotential lines or surfaces, and therefore no work is done in the direction of displacement. This concept is important in understanding the relationship between electric potential and electric fields, and it helps us visualize and analyze electric field distributions.

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