A square section wire of side L is traversed by a current I in the +z...

A square section wire of side L is traversed by a current I in the +z direction. The wire is embedded in a constant magnetic field B in the +y direction. You measure a voltage V across L in the horizontal direction. Find the number density of electrons in the metal and identify the direction of the electric field inside the wire.

Solutions

Expert Solution

Given,

A square section wire of side L placed in a region of magnetic field B(directed along +y direction) carrying a current I in +z direction.

The wires are metals and thus, will have only electrons as charge carriers.

A voltage V is measured along the horizontal direction (x-direction).

At equilibrium, the electric field produced by these displaced charges becomes equal to the magnetic force on them.

where, vd is the drift velocity of electrons in the material.

Width of the conductor is L. So the voltage developed will be

From the microscopic form of Ohm's law,the drift velocity can be expressed as

where, n = number density of electrons, q = charge of the electron and A is the area of cross-section = L2.

Comparing it will the equation for voltage, we get

So, the number density of electrons in the wire would be:

The potential difference (V) arises due to displacement of electrons along the +x-direction (from Fleming's Left hand rule). So, the direction of electric field will be along -x-direction.

This phenomenon is also called Hall effect and the voltage so developed is called the Hall voltage.

Regards

genius_generous answered 1 year ago

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