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The induced potential difference in a conductor moving through a magnetic field is directly proportional to:
The velocity of the conductor
The square of the magnetic field
The resistance of the conductor
The mass of the conductor
The velocity of the conductor
The induced potential difference (motional electromotive force) in a conductor moving through a magnetic field is directly proportional to the velocity of the conductor, the magnetic field strength, and the length of the conductor. This is a fundamental consequence of Faraday's law of electromagnetic induction applied to a moving conductor.
The induced potential difference (motional electromotive force) in a conductor moving through a magnetic field is directly proportional to the velocity of the conductor, the magnetic field strength, and the length of the conductor. This is a fundamental consequence of Faraday's law of electromagnetic induction applied to a moving conductor.
Think of it like pushing a gate through a strong wind; the faster you push the gate (v), the more air pressure you fight against, similar to how faster motion through a magnetic field 'pushes' more electrons to create a higher voltage.
B-L-V (B: Magnetic Field, L: Length, V: Velocity) тАФ all three factors directly boost the induced voltage.
E=BтЛЕlтЛЕvтЛЕsin(╬╕) тАФ Induced EMF where ╬╕ is the angle between velocity and magnetic field vectors
E=Blv тАФ Maximum induced EMF when motion is perpendicular to the field
When a conductor of length l moves with velocity v perpendicular to a magnetic field of strength B, the Lorentz force F=q(v├ЧB) acts on the free electrons within the conductor. This force drives the electrons to one end, creating a separation of charge that results in an induced potential difference (EMF) across the conductor's ends. This phenomenon is described by the motional EMF equation E=Blv.
The induced EMF is maximum when the velocity vector is perpendicular to the magnetic field.
If the conductor moves parallel to the magnetic field lines, the induced EMF is zero.
This principle is the foundation for electric generators and dynamos.
Enables conversion of mechanical energy into electrical energy.
Subject to energy losses due to eddy currents if the conductor is solid bulk metal.
AC and DC generators
Electromagnetic flowmeters
The relationship follows the right-hand rule for the direction of induced current.
Option B is incorrect because EMF is proportional to B, not B2.
Option C is incorrect because resistance affects the current (I=E/R), not the induced potential difference itself.
Option D is incorrect as mass does not appear in the motional EMF formula.
A is correct тАФ The induced potential difference is directly proportional to the velocity (v) of the conductor moving through a magnetic field as per the relation E=Blv.
Always remember that induced EMF depends on the rate of change of magnetic flux (d╬ж/dt); since v contributes to how fast the area is swept, it is directly proportional to the velocity.