A thin 2.82 m long copper rod in a uniform
magnetic field has a mass of 44.2 g. When the
rod carries a current of 0.238 A, it floats in
the magnetic field.
The acceleration of gravity is 9.81 m/s2 .
What is the field strength of the magnetic
field?
Answer in units of T.
F = IBL
F= mg
mg = IBL
B = mg / IL
( (0.0442 kg)(9.8 m/s^2) / (0.238 A)(2.82 m) )
= 0.646 T
To find the field strength of the magnetic field, we can use the formula for the force experienced by a current-carrying conductor in a magnetic field.
The formula is given by:
F = BIL
Where:
F is the force experienced by the conductor
B is the magnetic field strength
I is the current flowing through the conductor
L is the length of the conductor
Since the copper rod is floating in the magnetic field, we know that the force acting downwards due to gravity is balanced by the upward magnetic force.
The force due to gravity can be calculated using the formula:
F_gravity = mg
Where:
m is the mass of the copper rod
g is the acceleration due to gravity
In this case, m = 44.2 g = 0.0442 kg, and g = 9.81 m/s^2.
Since the rod is balanced in the magnetic field, we have F_gravity = F_magnetic.
So, we can equate the two formulas:
mg = BIL
Simplifying the equation, we can solve for B:
B = mg / (IL)
Now we can substitute the given values into the formula:
m = 0.0442 kg
g = 9.81 m/s^2
I = 0.238 A
L = 2.82 m
Plugging in these values, we get:
B = (0.0442 kg * 9.81 m/s^2) / (0.238 A * 2.82 m)
Simplifying further, we find:
B ≈ 0.073 T
Therefore, the field strength of the magnetic field is approximately 0.073 Tesla.
To find the magnetic field strength, we can use the equation:
F = BIL
Where F is the force on the rod, B is the magnetic field strength, I is the current, and L is the length of the rod.
Since the rod is floating in the magnetic field, the force acting on it is equal to the weight of the rod:
F = mg
where m is the mass of the rod and g is the acceleration due to gravity.
Substituting the values given:
mg = BIL
B = (mg) / (IL)
B = (0.0442 kg) * (9.81 m/s^2) / (0.238 A * 2.82 m)
B ≈ 0.750 T (Tesla)
Therefore, the magnetic field strength is approximately 0.750 T.