A Hall-effect probe operates with a 120 -mA current. When the probe is placed in a uniform magnetic field of magnitude 0.0840 T, it produces a Hall voltage of 0.660 µV. The thickness of the probe in the direction of B is 2.00 mm. Find the density of the charge carriers, each of which has charge of magnitude e).
I am using Vh = IB/net, where i can get the value for n.
the value of n is electrons/m^3
but the answer should be in m^-3.
Thank you
To find the density of the charge carriers, we can use the formula:
n = (I * B) / (e * Vh * t)
where:
n is the charge carrier density (in m^-3)
I is the current flowing through the probe (in Amperes)
B is the magnitude of the magnetic field (in Tesla)
e is the charge of each carrier (in Coulombs)
Vh is the Hall voltage measured (in Volts)
t is the thickness of the probe (in meters)
In this case, we have:
I = 120 mA = 120 * 10^-3 A
B = 0.0840 T
Vh = 0.660 µV = 0.660 * 10^-6 V
t = 2.00 mm = 2.00 * 10^-3 m (converted to meters)
Also, the charge of each carrier (e) is equal to the charge of an electron, which is approximately 1.6 * 10^-19 C.
Plugging in these values into the formula, we have:
n = (120 * 10^-3 A * 0.0840 T) / (1.6 * 10^-19 C * 0.660 * 10^-6 V * 2.00 * 10^-3 m)
Simplifying:
n ≈ 190.48 * 10^23 m^-3
Therefore, the density of the charge carriers is approximately 190.48 * 10^23 m^-3.