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Hall effect

Solid state phenomena · Physics

Study notes

Step 1: Consider a rectangular metal strip that is 2.0 cm wide, 5.0 cm long, and 0.1 cm thick. A current of 3.0 A flows along its length (from left to right). A uniform magnetic field of 0.50 T is applied perpendicular to the strip, pointing upward. Step 2: The Hall voltage (V_H) appears across the width of the strip. The formula for Hall voltage is V_H = (B * I) / (n * q * t), where: - B = magnetic field (0.50 T) - I = current (3.0 A) - n = charge carrier density (let’s assume 8.5×10^28 electrons/m^3 for copper) - q = elementary charge (1.60×10^-19 C) - t = thickness (0.1 cm = 0.001 m) Step 3: Plug the numbers in: V_H = (0.50 * 3.0) / (8.5×10^28 * 1.60×10^-19 * 0.001) V_H ≈ (1.5) / (1.36×10^9) V_H ≈ 1.1×10^-9 V or about 1.1 nV. Step 4: This tiny voltage is measurable with a sensitive voltmeter and tells us about the charge carriers in the metal.

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