A wire that is 46 cm long is parallel to a 0.54 T uniform magnetic field. The current through the wire is 4.5 A. What force acts on the wire?
remember 46 cm = .46 meters
then
http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/magnetic/forwir2.html
Now of course if the field is PARALLEL to the wire, sin of angle is 0 and the force is zero
To determine the force acting on the wire, you can use the formula for the magnetic force on a current-carrying wire in a magnetic field:
F = I * B * L * sinθ
Where:
F is the magnetic force
I is the current through the wire
B is the magnetic field
L is the length of the wire
θ is the angle between the direction of the current and the magnetic field
In this case, the wire is parallel to the magnetic field (θ = 0 degrees), so sinθ = 0.
Therefore, the magnetic force on the wire is:
F = I * B * L * 0 = 0
So, there is no force acting on the wire in this scenario since sinθ is zero.
To find the force acting on the wire, we can use the formula for the magnetic force on a current-carrying wire:
F = I * L * B * sin(θ)
Where:
F is the magnetic force,
I is the current through the wire,
L is the length of the wire,
B is the magnetic field strength, and
θ is the angle between the direction of the current and the magnetic field.
In this case, the length of the wire (L) is given as 46 cm, the current (I) is given as 4.5 A, and the magnetic field strength (B) is given as 0.54 T.
However, the angle (θ) between the direction of the current and the magnetic field is not given in the problem statement. In this case, we assume that the wire is perpendicular (θ = 90°) to the magnetic field, as it is stated that the wire is parallel to the magnetic field.
So, we have:
F = I * L * B * sin(90°)
Since sin(90°) = 1, we can simplify the equation to:
F = I * L * B
Now, we can substitute the given values into the equation:
F = 4.5 A * 0.46 m * 0.54 T
F = 1.2254 N
Therefore, the force acting on the wire is approximately 1.23 N.