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An infinitely long positively charged straight thread has a linear charge density λ C m⁻¹. An electron revolves along a circular path having its axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of the electron as a function of the radius of the circular path from the wire is

Asked in JEE Main 4th April 1st Shift 2024 · Charged cylinder and line charge

• (1) KE increases linearly with r, a straight line through the origin
• (2) KE stays constant, a horizontal line independent of r
• (3) KE falls off with r like a rectangular hyperbola
• (4) KE rises ever more steeply with r, curving upward

Step-by-step solution

Why the other options are wrong

• (1) Would follow if the attraction grew as r, i.e. for a field increasing with distance, which is not what a line charge gives.
• (3) Comes from equating (mv²)/r to (2kλ e)/(r²), i.e. using the point-charge 1/(r²) field instead of the line charge's 1/r field.
• (4) No attractive central force gives a kinetic energy that grows faster than linearly with the orbit radius.

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