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The force on a current-carrying conductor in a magnetic field is maximum when _____.
The current is parallel to the magnetic field
The current is perpendicular to the magnetic field
The current is opposite to the magnetic field
The magnetic field is zero
The current is parallel to the magnetic field
The force on a current-carrying conductor in a magnetic field is maximum when the conductor is placed perpendicular to the magnetic field. When the angle between the current flow and the magnetic field is 90┬░, the sine component of the force formula reaches its maximum value of 1.
The force on a current-carrying conductor in a magnetic field is maximum when the conductor is placed perpendicular to the magnetic field. When the angle between the current flow and the magnetic field is 90┬░, the sine component of the force formula reaches its maximum value of 1.
Think of catching a ball: if you hold your hand perfectly flat and perpendicular to the ball's path, you experience the maximum impact force, whereas if your hand moves parallel to the ball, you experience no impact.
Remember 'SIN' is for 'SINE': 90┬░ gives the maximum value (1) for sine, whereas 0┬░ gives zero.
F=ILBsin(╬╕) тАФ Force on a current-carrying conductor in a magnetic field
F=I(L├ЧB) тАФ Vector form of the force equation
The Lorentz force on a conductor is given by the cross product of current and magnetic field vectors. Because the magnitude is proportional to sin(╬╕), where ╬╕ is the angle between the length vector and the magnetic field vector, the force is zero when ╬╕=0┬░ (parallel) and maximum when ╬╕=90┬░ (perpendicular).
Maximum force occurs at ╬╕=90┬░ (sin(90┬░)=1)
Minimum force occurs at ╬╕=0┬░ or 180┬░ (sin(0)=0)
The direction of force is determined by Fleming's Left-Hand Rule
Underlies the operation of electric motors and galvanometers
DC Motors
Loudspeakers
The official answer key provided in the prompt is incorrect; the correct physical principle dictates that the force is maximum at 90┬░ (perpendicular).
Option A is incorrect because parallel current results in zero force.
Option C is incorrect because anti-parallel current results in zero force.
Option D is incorrect because no magnetic field results in no magnetic force.
B is correct тАФ The force on a current-carrying conductor in a magnetic field is maximum when the conductor is oriented perpendicular to the magnetic field.
Always check the sine component in physics formulas; sin(90┬░)=1 is your key to 'maximum' values, while sin(0┬░)=0 is your key to 'zero' or 'minimum' values.