If a conductor moves through a uniform magnetic field, the induced potential difference is maximised when ____

Question

If a conductor moves through a uniform magnetic field, the induced potential difference is maximised when _____.

Examoogle · Accepted Answer

The correct answer is Option D: the conductor is perpendicular to the magnetic field lines. The induced potential difference (electromotive force or EMF) across a moving conductor in a magnetic field is maximized when the conductor's velocity vector is perpendicular to the direction of the magnetic field lines. This is because the magnetic Lorentz force acting on the charge carriers is directly proportional to the sine of the angle between the velocity and the magnetic field.

Step-by-Step Solution & Concepts:
The induced potential difference (electromotive force or EMF) across a moving conductor in a magnetic field is maximized when the conductor's velocity vector is perpendicular to the direction of the magnetic field lines. This is because the magnetic Lorentz force acting on the charge carriers is directly proportional to the sine of the angle between the velocity and the magnetic field.

Working Principle: According to the principle of motional EMF, the force on a charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by $\vec{F} = q(\vec{v} 	imes \vec{B})$. The induced EMF is given by $\varepsilon = B l v \sin(	heta)$, where $	heta$ is the angle between the velocity vector and the magnetic field. Since $\sin(90^\circ) = 1$, the induced EMF is maximum when $	heta = 90^\circ$, meaning the conductor moves perpendicularly to the field lines.

Key Formulas: $\varepsilon = B l v \sin(	heta)$ — Motional EMF equation where $B$ is field strength, $l$ is length, $v$ is velocity, and $	heta$ is the angle.; $\vec{F} = q(\vec{v} 	imes \vec{B})$ — Lorentz force exerted on a moving charge in a magnetic field.

Key Points: The induced EMF is zero when the conductor moves parallel to the magnetic field ($\sin(0^\circ) = 0$).; The direction of the induced current is determined by Fleming's Right-Hand Rule.; Motional EMF is a practical application of the electromagnetic induction phenomenon.

Advantages: Fundamental principle behind electrical power generation in turbines.

Disadvantages: Induces eddy currents in solid conductors, which can cause unwanted heating (I^2R loss).

Applications: AC Generators (Alternators); Electromagnetic Flowmeters

Additional Info: The SI unit of induced EMF is the Volt (V).. Option C results in minimum (zero) induced EMF because the conductor does not 'cut' the magnetic field lines.. Option A is incorrect because the question specifies a uniform field; non-uniformity would introduce complexity but is not the condition for maximization.

Answer: D is correct — The induced potential difference is maximized when the conductor moves at a $90^\circ$ angle relative to the magnetic field lines because the sine of the angle is at its maximum value of 1.

Exam Tip: Always identify the angle between the velocity vector and the magnetic field vector in induction problems; if they are parallel, no EMF is generated, regardless of the field strength.

Examoogle · Answer

Option A: the magnetic field is non-uniform

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Option B: the magnetic field is zero

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Option C: the conductor is parallel to the magnetic field lines

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