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If the radius of the current carrying conductor increases, what is the effect on the force
increases
decreases
remain the same
become zero
remain the same
The magnetic force on a current-carrying straight conductor in a uniform magnetic field depends solely on the magnitude of current, the length of the conductor inside the field, the external magnetic flux density, and the angle between the conductor and the magnetic field. It is completely independent of the cross-sectional radius or physical thickness of the conductor. Therefore, increasing the radius of the conductor leaves the net magnetic force unchanged.
The magnetic force on a current-carrying straight conductor in a uniform magnetic field depends solely on the magnitude of current, the length of the conductor inside the field, the external magnetic flux density, and the angle between the conductor and the magnetic field. It is completely independent of the cross-sectional radius or physical thickness of the conductor. Therefore, increasing the radius of the conductor leaves the net magnetic force unchanged.
F=ILBsin╬╕ тАФ Magnetic force on a straight current-carrying conductor
I=nqAvdтАЛ тАФ Relationship between current, cross-sectional area A, and drift velocity vdтАЛ
When charges move through a conductor immersed in an external magnetic field, each individual moving charge experiences a microscopic Lorentz force. The total macroscopic magnetic force exerted on the conductor is the vector sum of these individual microscopic forces over the entire active volume. Because the total current I represents the total charge flowing per unit time across the cross-section (I=nqAvdтАЛ), any change in cross-sectional area A due to a altered radius changes the drift velocity vdтАЛ inversely, keeping the total macroscopic product I=nqAvdтАЛ and resulting force F constant.
The force F is directly proportional to current I, conductor length L, and magnetic flux density B.
Conductor radius or cross-sectional area A does not feature in the standard magnetic force equation F=ILBsin╬╕.
Increasing conductor radius decreases resistance and drift velocity for a given current, but the total Lorentz force on the entire current remains unchanged.
Option A (increases) is incorrect because force does not depend directly or inversely on cross-sectional dimensions.
Option B (decreases) is incorrect as force relies on net charge flow rate I, not the individual wire radius.
Option D (become zero) is incorrect because force becomes zero only if I=0, B=0, L=0, or ╬╕=0┬░/180┬░.
C is correct тАФ The magnetic force depends on current, length, and magnetic field strength, making it independent of conductor radius.
In competitive exams, always check whether the parameter being modified (like conductor radius) explicitly appears in the core formula (F=ILBsin╬╕) before selecting an option.