Question

# A current-carrying conductor placed in a magnetic field experiences a force. The displacement of the conductor in the magnetic field can be increased by

A

Decreasing the magnetic field

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B

Decreasing the current in the conductor

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C

Increasing the magnetic field

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D

None of the above

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Solution

## The correct option is C Increasing the magnetic fieldThe explanation for the correct optionC: Increasing the magnetic field The interaction between the magnetic field lines of the magnet and the conductor causes a magnetic force on the conductor.If ($L$) represents the length of the conductor, ($i$) represents the current flowing through the conductor, ($B$) represents the strength of the magnetic field, then the magnetic force ($F$) experienced by the conductor is given by$F=i×L×B$From the above equation, it is clear that the magnetic force experienced by a current-carrying conductor placed in a magnetic field is directly proportional to the strength of the magnetic field.$F\propto B$ …………………….(a)The magnetic force experienced by the conductor will cause displacement ($d$) in the conductor because the force has the inherent property of causing displacement.From the basic crux of Newton's law of motion, the more the magnetic force experienced by the current-carrying conductor, the more will be its displacement.$d\propto F$ …………………..(b)Comparing equations (a) and (b), we can conclude$d\propto B$Hence, the displacement of the current-carrying conductor placed in a magnetic field is directly proportional to the strength of the magnetic field.More the strength of the magnetic field, the more will be the displacement of the conductor and vice versa.The explanation for the incorrect optionB: Decreasing the current in the conductorMagnetic force experienced by a current-carrying conductor placed in a magnetic field is directly proportional to the electric current flowing through the conductor.$F\propto i$ …………………….(c)Logically speaking, the more the magnetic force experienced by the conductor, the more will be its displacement.$d\propto F$ …………………(d)From equations (c) and (d), we can conclude$d\propto i$Hence, the more the current flowing through the conductor placed in a magnetic field, the more will be its displacement and vice versa.Decreasing the current will decrease the displacement of the conductor.Hence, option (c) is correct.

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