Question: A wire segment of length 0.5 m carrying a current of 2 A is placed perpendicular to a uniform magnetic field of 0.8 T. Calculate the magnitude and direction of the force acting on the wire segment.
Answer: To calculate the magnitude and direction of the force acting on the wire segment, we can use the formula for the force on a current-carrying conductor in a magnetic field:
F = I * L * B * sin(θ)
where: F = force I = current L = length of the wire segment B = magnetic field strength θ = angle between the direction of the current and the magnetic field
Given: I = 2 A L = 0.5 m B = 0.8 T
First, let's calculate the angle θ between the direction of the current and the magnetic field. Since the wire segment is placed perpendicular to the magnetic field, θ = 90 degrees.
Now, plug in the values into the formula:
F = 2 A * 0.5 m * 0.8 T * sin(90°) = 2 A * 0.5 m * 0.8 T * 1 = 0.8 N
The magnitude of the force acting on the wire segment is 0.8 N.
Next, let's determine the direction of the force using the right-hand rule. Point your right thumb in the direction of the current and your fingers in the direction of the magnetic field. Your palm will face the direction of the force. In this case, the force will be directed downward.
Therefore, the magnitude of the force acting on the wire segment is 0.8 N in the downward direction.