Question:
A wire of length 2.5 meters is bent into a square with sides of equal length. The wire carries a current of 5.0 Amperes. A magnetic field of 0.3 Tesla is applied perpendicular to the plane of the square. Calculate the magnitude and direction of the magnetic force acting on one side of the square.
Answer:
To find the magnitude and direction of the magnetic force acting on one side of the square, we can use the formula for magnetic force:
F = I * L * B * sinθ
Where:
In this case, we have a square wire, so one side of the square will have a length equal to the length of the wire (2.5 meters). The current in the wire is given as 5.0 Amperes, and the magnetic field strength is given as 0.3 Tesla.
First, let's find the angle θ. Since the wire is perpendicular to the magnetic field, the angle between the direction of the current and the magnetic field is 90 degrees (π/2 radians).
Now, we can substitute the given values into the formula and calculate the magnetic force:
F = (5.0 A) * (2.5 m) * (0.3 T) * sin(π/2)
To find sin(π/2), we know that sin(90 degrees) is equal to 1.
F = (5.0 A) * (2.5 m) * (0.3 T) * 1
Simplifying the expression:
F = 3.75 Newtons
Therefore, the magnitude of the magnetic force acting on one side of the square wire is 3.75 Newtons. Since the wire carries a current in a clockwise direction (considering the direction of the current flow in the square), the magnetic force will act in the direction perpendicular to both the current and the magnetic field, i.e. outwards from the plane of the square.
Thus, the direction of the magnetic force acting on one side of the square wire is outwards from the plane of the square.
Note: The direction of the magnetic force can also be determined by the right-hand rule, where the thumb represents the direction of the current, the fingers represent the magnetic field, and the palm represents the direction of the magnetic force.