A wire of length 0.655m carries a current of 21.0A. In the presence of a 0.470-T magnetic field, the wire experiences a force of 5.46N. What is the angle (less than 90degrees) between the wire and the magnetic field？
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To find the angle between the wire and the magnetic field, we can use the formula for the magnetic force on a current-carrying wire:
F = I * L * B * sin(θ)
where:
F is the force on the wire,
I is the current flowing through the wire,
L is the length of the wire,
B is the magnetic field strength, and
θ is the angle between the wire and the magnetic field.
In this problem, we are given:
L = 0.655 m (length of the wire)
I = 21.0 A (current flowing through the wire)
B = 0.470 T (magnetic field strength)
F = 5.46 N (force on the wire)
Rearranging the formula, we can solve for the angle (θ):
θ = arcsin(F / (I * L * B))
Now, let's substitute the given values into the formula and solve for the angle:
θ = arcsin(5.46 N / (21.0 A * 0.655 m * 0.470 T))
Using a calculator, we can find that the angle (θ) is approximately 35.1 degrees.
Therefore, the angle between the wire and the magnetic field is 35.1 degrees.
To find the angle between the wire and the magnetic field, we can use the formula for the force on a current-carrying wire in a magnetic field.
The formula is given by:
F = BILsin(θ)
Where:
F = Force
B = Magnetic Field Strength
I = Current
L = Length of the wire
θ = Angle between the wire and the magnetic field
In this case, we are given the following values:
F = 5.46N
B = 0.470T
I = 21.0A
L = 0.655m
We need to rearrange the formula to solve for the angle (θ).
Dividing both sides by (BIL), we get:
θ = sin^(-1)(F / (BIL))
Now, we can substitute the given values into the formula:
θ = sin^(-1)(5.46N / (0.470T * 21.0A * 0.655m))
Using a calculator, we can find the value of the angle:
θ ≈ sin^(-1)(0.177)
In degrees, the angle is:
θ ≈ 10.202°
Therefore, the angle between the wire and the magnetic field is approximately 10.202°.