A thin, 8.3 m long copper rod in a uniform magnetic field has a mass of 68 g. When the rod carries a current of .343 A, it floats in the magnetic field. What is the field strength of the magnetic field?
To find the field strength of the magnetic field, given the information about the copper rod, we can use the principle of magnetic levitation.
First, let's analyze the forces acting on the copper rod. When an electric current flows through a conductor such as the copper rod, a magnetic field is created around the conductor. This magnetic field interacts with the external magnetic field, resulting in a force called the magnetic force.
In this case, the rod is floating, so the gravitational force acting downward is equal to the magnetic force acting upward. Therefore, we can set up an equation for the forces:
Magnetic force = Gravitational force
The magnetic force can be calculated using the formula:
Magnetic force = BIL
where B is the magnetic field strength, I is the current flowing through the rod, and L is the length of the rod.
The gravitational force can be calculated using the formula:
Gravitational force = mass × acceleration due to gravity
We can rearrange the equation for the magnetic force to solve for the magnetic field strength:
B = (Gravitational force) / (IL)
Now, let's substitute the given values into the equation:
Mass = 68 g = 0.068 kg (convert grams to kilograms)
Length of the rod, L = 8.3 m
Current, I = 0.343 A
Acceleration due to gravity can be assumed as 9.8 m/s².
Plugging in the values:
B = (0.068 kg × 9.8 m/s²) / (0.343 A × 8.3 m)
Now we can calculate the magnetic field strength. Evaluating the expression:
B = 0.679 T (rounded to three decimal places)
Therefore, the field strength of the magnetic field is approximately 0.679 Tesla (T).