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  • An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another.

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another.
This is because,
(a) the two magnetic forces are equal and opposite, so they produce no net effect.
(b) the magnetic forces do no work on each particle.
(c) the magnetic forces do equal and opposite (but non-zero) work on each particle.
(d) the magnetic forces are necessarily negligible.

Answers (1)

The answer is option (b) the magnetic forces do not work on each particle.

The concept used in this question is of the work-energy theorem. According to which, net work done = (change in kinetic energy). Final kinetic energy – Initial kinetic energy of the object.

\sum W = K_{f} - K_{i}

The direction of the magnetic forces will be at an angle of 90 degrees to the motion of the electron and proton under mutual forces. As a result, the magnetic force acts like a centripetal force which leads the particles to undergo uniform circular motion. Hence, their speed remains constant throughout the motion. Since the speed is constant, the kinetic energy remains the same, and hence the net work done due to the change in kinetic energy by the forces amounts to zero. By the formula, we know that: \overrightarrow{Fm }= q. (\overrightarrow{v} \times \overrightarrow{ B}). , B is the external magnetic field, and v is the velocity of the particle. Hence, we can ignore the magnetic force of one particle on another.

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