The force on a wire is a maximum of 6.5E-2 N when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to "jump" toward the observer when the current is turned on. If the pole faces have a diameter of 17.5 cm, estimate the current in the wire if the field is 0.24 T.
If the wire is tipped so that it makes an angle of 22.0° with the horizontal, what force will it now feel?
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To find the current in the wire, we can use the formula for the force on a wire in a magnetic field:
F = BILsinθ
Where:
- F is the force on the wire
- B is the magnetic field strength
- I is the current in the wire
- L is the length of the wire
- θ is the angle between the wire and the magnetic field
Given:
- The maximum force on the wire is 6.5E-2 N
- The magnetic field strength is 0.24 T
- The angle between the wire and the magnetic field is 22.0°
First, let's determine the length of the wire. Looking at the problem statement, we can see that the wire is placed between the pole faces of a magnet. Given the diameter of the pole faces, we can calculate the radius:
Radius (r) = Diameter / 2 = 17.5 cm / 2 = 8.75 cm = 0.0875 m
Since the wire is placed between the pole faces, we can estimate the length of the wire to be approximately equal to the circumference of the pole face:
Circumference (C) = 2πr = 2π(0.0875 m) = 0.549 m
Now we can solve for the current by rearranging the formula:
I = F / (B * L * sinθ)
I = 6.5E-2 N / (0.24 T * 0.549 m * sin(22.0°))
I ≈ 1.561 A (rounded to three decimal places)
Therefore, the estimated current in the wire is approximately 1.561 A.
Now, let's move on to the second part of the question.
If the wire is tipped so that it makes an angle of 22.0° with the horizontal, we need to find the new force acting on the wire.
Using the same formula, F = BILsinθ, we can substitute the values:
F = (0.24 T) * (1.561 A) * (0.549 m) * sin(22.0°)
F ≈ 0.099 N (rounded to three decimal places)
Therefore, the wire will now feel a force of approximately 0.099 N.