The question contains Statement I and Statement II. Of the...

The question contains Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement I For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$. Statement II The net work done by a conservative force on an object moving along a closed loop is zero. [AIEEE 2009] (a) Statement 1 is true, Statement 11 is false (b) Statement 1 is true, Statement II is true, Statement II is the correct explanation of Statement 1 (c) Statement 1 is true, Statement 11 is true, Statement 11 is not the correct explanation of Statement 1 (d) Statement 1 is false, Statement $\|$ is true

The question contains Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement I For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.
Statement II The net work done by a conservative force on an object moving along a closed loop is zero. [AIEEE 2009]
(a) Statement 1 is true, Statement 11 is false
(b) Statement 1 is true, Statement II is true, Statement II is the correct explanation of Statement 1
(c) Statement 1 is true, Statement 11 is true, Statement 11 is not the correct explanation of Statement 1
(d) Statement 1 is false, Statement $\|$ is true

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Key Concepts

Zero Work in Closed Paths

For any conservative force, the net work done on an object that undergoes a complete closed-loop journey is zero. This stems from the idea that, since the work depends only on the starting and ending points, and these points coincide in a closed loop, the work done must cancel out to zero.

Path Independence of Work

Path independence refers to the property where the net work done by a conservative force on an object moving between any two specific points is solely a function of those points and not of the particular route taken. This is a fundamental characteristic of conservative forces like electrostatic and gravitational forces.

Conservative Forces

A conservative force is one for which the work done in moving an object between two points is independent of the path taken. This characteristic implies the existence of a potential energy function, and as a consequence, the work done over any closed path is zero. Common examples include gravitational and electrostatic forces.

Electrostatic Fields

Electrostatic fields, generated by stationary charges, are inherently conservative. This means that the work done by an electrostatic force when moving a charged particle between two points depends solely on the initial and final positions, not on the trajectory followed.

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