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 equation:
Vh = IB / (net)
where:
Vh = Hall voltage = 0.660 µV = 0.660 x 10^-6 V
I = current = 120 mA = 120 x 10^-3 A
B = magnetic field = 0.0840 T
e = magnitude of charge of each carrier = 1.6 x 10^-19 C (elementary charge)
The thickness of the probe (t) is given as 2.00 mm = 2.00 x 10^-3 m.
Now, let's calculate the value of n (number density of charge carriers):
n = (Vh x net) / (I x B)
First, let's find the net (proportional to the thickness t):
net = t / e
net = 2.00 x 10^-3 m / (1.6 x 10^-19 C)
net = 1.25 x 10^16 m^-2
Now, substitute the given values into the equation:
n = (0.660 x 10^-6 V x 1.25 x 10^16 m^-2) / (120 x 10^-3 A x 0.0840 T)
n = (8.25 x 10^-22 m^-1) / (1.008 x 10^-2 A.T)
n = 8.17 x 10^19 m^-3
Therefore, the density of the charge carriers is approximately 8.17 x 10^19 m^-3.
To find the density of the charge carriers, you can use the equation:
n = (IB)/(eVh)
Where:
- n is the density of the charge carriers (in m^-3)
- I is the current in the Hall-effect probe (in A)
- B is the magnitude of the magnetic field (in T)
- e is the charge of an electron (1.6 x 10^-19 C, in this case)
- Vh is the Hall voltage (in V)
First, convert the given current into Amperes:
120 mA = 120 x 10^-3 A = 0.120 A
Next, convert the thickness of the probe into meters:
2.00 mm = 2.00 x 10^-3 m
Now, substitute the given values into the equation:
n = (0.120 A * 0.0840 T) / (1.6 x 10^-19 C * 0.660 x 10^-6 V)
Simplify the equation:
n = (0.01008 A⋅T) / (1.056 x 10^-25 C⋅V)
n = 9.5 x 10^24 m^-3
Therefore, the density of the charge carriers (electrons) is approximately 9.5 x 10^24 m^-3.