A straight horizontal rod A of mass 50 gm and length 0.5 m, is placed in a uniform horizontal magnetic field of 0.2 T, perpendicular to A. Calculate the current in A if the force acting on it just balances it weight.
Require that
M g = B I L
Solve for I (amps). Make sure M is in kg.
I = M g/(B L)
To calculate the current in the straight rod, we need to use the formula for the force acting on a current-carrying wire in a magnetic field.
The formula is given by:
F = BIL
Where:
F is the force on the wire,
B is the magnetic field strength,
I is the current flowing through the wire, and
L is the length of the wire in the magnetic field.
In this case, we know the following values:
B = 0.2 T (the magnetic field strength),
L = 0.5 m (the length of the rod).
We need to find the value of I (the current).
The force acting on the rod is balanced by its weight, which is given by:
Force = mass * acceleration due to gravity
Given that the mass of the rod is 50 gm (0.05 kg) and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the force as follows:
Force = 0.05 kg * 9.8 m/s²
Now, equating this force to the force in the magnetic field, we have:
Force = BIL
0.05 kg * 9.8 m/s² = 0.2 T * I * 0.5 m
Simplifying the equation:
0.049 N = 0.1 T * I
Solving for I:
I = 0.049 N / (0.1 T * 0.5 m)
I = 0.049 N / 0.05 T
I = 0.98 A
Therefore, the current in rod A is 0.98 Amperes.