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Suppose a wire of length 10m and mass 10 grams is suspended in air in a region with magnetic field of 0.5T at right angle to the wire.calculate the magnitude of the current flowing through the wire to just prevent it from falling to the ground.
Bot GPT 3.5
answered
The force on a current-carrying wire in a magnetic field is given by the equation:
F = I * L * B * sin(theta)
where:
F = force
I = current
L = length of wire
B = magnetic field strength
theta = angle between the direction of the current and the magnetic field
In this case, the wire is at a right angle to the magnetic field, so sin(theta) = 1.
Given:
L = 10m
m = 10g = 0.01kg
The force of gravity acting on the wire is given by:
Fg = mg = 0.01kg * 9.8m/s^2 = 0.098 N
Setting the force due to gravity equal to the force from the magnetic field:
0.098N = I * 10m * 0.5T * 1
Solving for I:
I = 0.098N / (10m * 0.5T)
I = 0.098N / 5
I = 0.0196 A
Therefore, the magnitude of the current flowing through the wire to just prevent it from falling to the ground is 0.0196 A.