Question

In the Hall effect, a potential difference produced across a conductor of finite thickness in a magnetic field by a current flowing through the conductor is given by a) the product of the density of electrons, the charge of an electron, and the conductor's thickness divided by the product of the magnitudes of the current and the magnetic field. b) the reciprocal of the expression described in part (a). c) the product of the charge on an electron and the conductor's thickness divided by the product of the density of electrons and the magnitudes of the current and the magnetic field. d) the reciprocal of the expression described in (c). e) none of the above.

Short answer

a) the product of the density of electrons, the charge of an electron, and the conductor's thickness divided by the product of the magnitudes of the current and the magnetic field. b) the reciprocal of the expression described in part (a) c) the product of the charge on an electron and the conductor's thickness divided by the product of the density of electrons and the magnitudes of the current and the magnetic field. d) the reciprocal of the expression described in (c) e) none of the above Answer: e) none of the above.

Step-by-step solution

Understand the Hall effect

The Hall effect occurs when a current-carrying conductor is placed in a magnetic field. A potential difference called the Hall voltage develops across the conductor due to the force exerted by the magnetic field on the moving electrons. The Hall effect formula is given by: Hall voltage (V_H) = (I * B * t) / (q * n * A) Where: - I is the current flowing through the conductor, - B is the magnetic field, - t is the thickness of the conductor, - q is the charge of an electron, - n is the number of charge carriers (density of electrons) per unit volume, and - A is the cross-sectional area of the conductor. Step 2: Analyze the given options

Analyze the options

Now, let's see which of the given options corresponds to the correct expression of the Hall voltage. a) the product of the density of electrons, the charge of an electron, and the conductor's thickness divided by the product of the magnitudes of the current and the magnetic field. The expression is: (n * q * t) / (I * B) Comparing with Hall voltage formula, this expression is incorrect. b) the reciprocal of the expression described in part (a) The expression is: (I * B) / (n * q * t) Comparing with the Hall voltage formula, this expression is incorrect. c) the product of the charge on an electron and the conductor's thickness divided by the product of the density of electrons and the magnitudes of the current and the magnetic field. The expression is: (q * t) / (n * I * B) Comparing with the Hall voltage formula, this expression is incorrect. d) the reciprocal of the expression described in (c) The expression is: (n * I * B) / (q * t) Comparing with the Hall voltage formula, this expression is correct, but since 'A' is missing from the denominator, it is incorrect. e) none of the above As none of the given expressions in options a, b, c, and d are correct, the correct answer is: Answer: e) none of the above.