A wire of length 0.655 m carries a current of 21.0 A. In the presence of a 0.470-T magnetic field, the wire experiences a force of 5.46 N. What is the angle (less than 90°) between the wire and the magnetic field?
Force=ILB sinTheta
solve for Theta.
in my head, I get about 60 deg.
To find the angle between the wire and the magnetic field, we can use the formula for the magnetic force experienced by a wire:
F = BILsinθ
Where:
F = Force experienced by the wire (in Newtons)
B = Magnetic field strength (in Tesla)
I = Current flowing through the wire (in Amperes)
L = Length of the wire (in meters)
θ = Angle between the wire and the magnetic field (in degrees)
We are given:
F = 5.46 N
B = 0.470 T
I = 21.0 A
L = 0.655 m
Now, let's rearrange the formula to solve for θ:
θ = arcsin(F / (BIL))
Plugging in the given values:
θ = arcsin(5.46 N / (0.470 T * 21.0 A * 0.655 m))
Using a calculator or a trigonometric table, we can evaluate the arcsin function to find the angle.
Note: Make sure your calculator is in degree mode. If it's in radian mode, convert the answer from radians to degrees.
Therefore, the angle (less than 90°) between the wire and the magnetic field can be found by evaluating the above expression using a calculator or trigonometric table.