# Hall Voltage Calculator, Formula, Hall Voltage Calculation

## Hall Voltage Calculator:

Enter the values of current, I(A), magnetic field, B(T), density of mobile charges, n(carriers/m3), elementary charges, e(C) and thickness of the material, d(m) to determine the value of hall voltage, Vh(V).

 Enter Current: A Enter Magnetic Field: T Enter Density of Mobile Charges: carriers/m3 Enter Elementary Charges: c Enter Thickness: m Result – Hall Voltage: V

## Hall Voltage Formula:

Hall voltage is a key concept in semiconductor physics and electrical engineering, primarily observed in the Hall effect.

The Hall effect occurs when a current-carrying conductor or semiconductor is placed in a perpendicular magnetic field, resulting in the development of a voltage (Hall voltage) across the material.

This voltage is perpendicular to both the current and the magnetic field.

The Hall voltage is crucial for determining carrier concentration, type of charge carriers, and magnetic field strength in materials.

Hall voltage, Vh(V) in volts is calculated by dividing the product of current, I(A) in amperes and magnetic field, B(T) in tesla by the product of density of mobile charges, n(carriers/m3) in carriers per cubic metres, elementary charges, e(C) in coulombs and thickness of the material, d(m) in metres.

Hall voltage, Vh(V) = I(A) * B(T) / n(carriers/m3) * e(C) * d(m)

Vh(V) = hall voltage in volts, V.

I(A) = current in amperes, A.

B(T) = magnetic field in tesla, T.

n(carriers/m3) = density of mobile charges in carriers per cubic metres.

e(C) = elementary charges, C.

d(m) = thickness in metres, m.

### Hall Voltage Calculation:

1. Calculate the Hall voltage for a current of 5 amperes, a magnetic field of 0.2 tesla, a charge carrier density of 1 * 1022 carriers per cubic meter, and a material thickness of 0.01 metres:

Given: I(A) = 5A, B(T) = 0.2T, n(carriers/m3) = 1 * 1022, e(C) = 1.6 * 10-19, d(m) = 0.01m.

Hall voltage, Vh(V) = I(A) * B(T) / n(carriers/m3) * e(C) * d(m)

Vh(V) = 5 * 0.2 / 1 * 1022 * 1.6 * 10-19 * 0.01

Vh(V) = 1 / 1.6 * 10

Vh(V) = 0.0625V.

1. Determine the thickness for a current of 10 amperes, a magnetic field of 0.5 tesla, a charge carrier density of 5 * 1021 carriers per cubic metre, a material thickness of 0.02 meters and the acquired hall voltage is 0.03125V.

Given: I(A) = 10A, B(T) = 0.5T, n(carriers/m3) = 5 * 1021, e(C) = 1.6 * 10-19, Vh(V) = 0.03125V.

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Hall voltage, Vh(V) = I(A) * B(T) / n(carriers/m3) * e(C) * d(m)

d(m) = I(A) * B(T) / n(carriers/m3) * e(C) * Vh(V)

d(m) = 10 * 0.5 / 5 * 1021 * 1.6 * 10-19 * 0.03125

d(m) = 5 / 2500

d(m) = 0.002m.

### Applications and Considerations:

• Semiconductor Characterization: Hall voltage measurements are essential for determining the type and concentration of charge carriers in semiconductors.
• Magnetic Field Sensors: Hall effect sensors are widely used to measure magnetic field strength in various applications, including automotive and industrial systems.