A straight horizontal rod x,of mass 50g and length 0.5m, is placed in a uniform field of 0.2T perpendicular to x. Calculate the current in x if the force acting on it just balance it weight.
wonder what perpendicular to a rod means...somehow it needs to be in the right direction.
Grace
To calculate the current in the rod x, we need to use the equation that relates the force on a current-carrying conductor in a magnetic field to the current and other known quantities.
The equation is: F = BIL, where F is the force, B is the magnetic field strength, I is the current, and L is the length of the conductor.
Given:
- Mass of the rod, m = 50g = 0.05kg
- Length of the rod, L = 0.5m
- Magnetic field strength, B = 0.2T
We need to find the current, I, that will balance the weight of the rod.
1. Calculate the weight of the rod:
Weight = mass * gravitational acceleration
Weight = 0.05kg * 9.8m/s^2
2. Since the force required to balance the weight is the magnetic force, let's set the two equal:
F = Weight = BIL
3. Rearrange the equation to solve for the current, I:
I = Weight / (B * L)
Substitute the given values into the equation:
I = (0.05kg * 9.8m/s^2) / (0.2T * 0.5m)
4. Solve for I:
I = (0.49 kg·m/s^2) / (0.1 T·m)
I = 4.9 A
The current in the rod x is 4.9 Amperes.