The field-line representation of the electric field in a certain region of space

Question

The field-line representation of the electric field in a certain region of space is shown above.  The dashed lines represent equipotential lines.

Question 1: At which point (A-D) in space is the electric field the weakest?

Question 2: Compare the work done moving a negative charge from A to B and from A to D. Which one requires more work?

(A) More work is required to move a negative charge from A to B than from A to D
(B) More work is required to move a negative charge from A to D than from A to B
(C) The same amount of work is required to move a negative charge from A to B as to move it from A to D
(D) Cannot determine without performing the calculation

The field-line representation of the electric field in a certain region of space is shown above. The dashed lines represent equipotential lines. At which point (A-D) in space is the electric field the weakest? Compare the work done moving a negative charge from A to B and from A to D. Which one requires more work? More work is required to move a negative charge from A to B than from A to D More work is required to move a negative charge from A to D than from A to B The same amount of work is required to move a negative charge from A to B as to move it from A to D Cannot determine without performing the calculation

Explanation / Answer

1) electric field is weakest where the field lines are the least dense

hence answer is option (D)

2) the same amount of work is needed

this can be explained as follows:

we know that electrostatic work is path independent, hence is the same for all paths that we choose.

hence for moving from A to D, we first move from A to B and then from B to D. now as B and D are equipotential, hence no work is done while moving along the equipotential line. hence, resultant amount is the same as while moving from A to B.

Hence correct answer is option (c)

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