Hall effect in conductors and semiconductors A specimen (metal or semiconductor) carries an electric current and is placed in a uniform magnetic field. Due to charge deflection, a transverse “Hall” electric field develops inside the specimen. What is the direction of this resultant electric field?

Introduction / Context:
The Hall effect is a foundational phenomenon in solid-state physics and electrical engineering. When an electric current flows through a conductor or semiconductor placed in a magnetic field, moving charge carriers experience a magnetic force that pushes them sideways, creating a measurable transverse voltage called the Hall voltage. Understanding the direction of the resulting internal electric field is essential for sensor design and for determining carrier type and mobility.

Given Data / Assumptions:

• Uniform current density flows along the length of the specimen.
• A steady magnetic field is applied at right angles to the current direction.
• Charge carriers are either electrons or holes; sign affects polarity but not orthogonality of directions.
• Specimen has ohmic contacts and a rectangular geometry for clarity.

Concept / Approach:

The Lorentz force on a carrier of charge q moving with drift velocity v in magnetic field B is F = q (v × B). This force deflects carriers to one side, causing charge separation. The separation builds a transverse electric field EH that opposes further deflection. At equilibrium, q EH balances q (v × B), making EH perpendicular to both current (direction of v) and magnetic field B.

Step-by-Step Solution:

Verification / Alternative check:

Polarity of the Hall voltage reverses when carrier type changes (electrons vs. holes) or when B direction flips, but the orthogonality remains: the Hall field is always transverse to both current and magnetic field.

Why Other Options Are Wrong:

Along current (b) or parallel/anti-parallel to B (c, e) contradicts v × B geometry; “None” (d) ignores the well-established perpendicular Hall field.

Common Pitfalls:

Confusing the direction of EH with its polarity; forgetting that EH vanishes if either current or B is zero; overlooking that contact placement determines the measured Hall voltage sign.

Final Answer:

Normal (perpendicular) to both the current and the magnetic field