A current of 2.7 A flows in a straight wire segment of length (2.5 cm) ˆı + (2.5 cm) ˆ in a uniform magnetic field of strength (1.7 T) ˆı . Find the magnitude of the force on the wire.
Well, well, well, it seems like we have a shocking situation here, doesn't it? Let me calculate the force for you and amp up the humor while we're at it!
To find the force on the wire, we can use the formula F = I * L * B * sin(θ), where F is the force, I is the current, L is the length of the wire segment, B is the magnetic field strength, and θ is the angle between the current and the magnetic field.
Since the wire is straight, the angle between the current and the magnetic field is 0 degrees (cosine of 0 is 1), meaning sin(θ) is 0. Therefore, the force on the wire will be 0 N.
Oops, that's not what you were expecting, huh? Don't worry, this is just a little magnetic joke! The magnitude of the force is actually given by F = I * L * B. Plugging in the values, we get:
F = (2.7 A) * (2.5 cm) * (1.7 T)
Doing the math, we find:
F ≈ 11.475 N
So, the magnitude of the force on the wire is approximately 11.475 N. And remember, no need to get current-ed up about it, it's just the wires being magnetically attractive!
To find the magnitude of the force on the wire, we can use the formula for the force experienced by a current-carrying wire in a magnetic field:
F = I * L * B * sin(θ)
Where:
F is the magnitude of the force on the wire,
I is the current in the wire,
L is the length of the wire segment,
B is the magnetic field strength,
θ is the angle between the direction of the current and the magnetic field.
In this case, the current in the wire is given as 2.7 A, the length of the wire segment is 2.5 cm in the x-direction and 2.5 cm in the y-direction, and the magnetic field strength is given as 1.7 T in the x-direction.
First, we need to calculate the angle θ between the current and the magnetic field direction. Since the wire segment is in the x-y plane and the magnetic field is in the x-direction, the angle between them is 90 degrees or π/2 radians.
Substituting the given values into the formula, we have:
F = (2.7 A) * ((2.5 cm) ˆı + (2.5 cm) ˆ) * (1.7 T) * sin(π/2)
To simplify the calculation, let's convert the length from centimeters to meters:
L = (2.5 cm) * (0.01 m/cm) = 0.025 m
Now we can substitute the values into the formula:
F = (2.7 A) * (0.025 m) * (1.7 T) * sin(π/2)
Since sin(π/2) = 1, the formula becomes:
F = (2.7 A) * (0.025 m) * (1.7 T) * 1
Calculating this expression gives us the magnitude of the force on the wire.