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In order to double the energy gained by a charge , how much times magnetic field should be increased?
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In order to double the energy gained by a charge , how much times magn...
One is that the kinetic energy will not change since the magnetic force is necessarily perpendicular to the velocity according to the mathematics of the best theories of electromagnetism. Net forces perpendicular to velocities change directions of motion without changing speed. But any change in velocity, including a change in direction of motion, is acceleration.

Accelerating charged particles radiate electromagnetic energy and thereby slow down. There are exceptions to this if there is no lower energy level available to the charged particles. If the charged particles do continuously slow down this way, they will spiral inward while moving slower and slower.
However, the question specifically indicates a “charged body.” It is possible that this would be about a macroscopic object that happens to have a net charge. It would likely be moving slowly compared to typical speeds of electrons or ions in particle beams. In that case the accelerations would be very small, and the loss in speed would likely not be noticeable for a long time.
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In order to double the energy gained by a charge , how much times magnetic field should be increased?
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