Consider a wire of length L = 0.30 m that runs north-south on a horizontal surface. There is a current of I = 0.50 A flowing north in the wire. (The rest of the circuit, which actually delivers this current, is not shown.) The Earth's magnetic field at this location has a magnitude of 0.50 {\rm gauss} (or, in SI units, 0.5 \times 10^{-4} \; \rm tesla) and points north and 38 degrees down from the horizontal, toward the ground. What is the size of the magnetic force on the wire due to the Earth's magnetic field? In considering the agreement of units, recall that 1\;{\rm T} = 1\;{\rm N / (\rm A \cdot \rm m)}
This question is actually more simple than it seems. You just use the equation F=ILBsin(theta) with theta in radians. The answer is 4.6*10^(-6)N
To find the size of the magnetic force on the wire due to the Earth's magnetic field, we can use the formula for the magnetic force on a current-carrying wire:
F = I * L * B * sin(theta)
where:
F is the magnetic force on the wire,
I is the current flowing through the wire,
L is the length of the wire,
B is the magnitude of the magnetic field, and
theta is the angle between the direction of the current and the magnetic field vector.
Plugging in the given values:
I = 0.50 A (current flowing north)
L = 0.30 m (length of the wire)
B = 0.5 * 10^(-4) T (magnitude of the Earth's magnetic field)
theta = 38 degrees
First, we need to convert theta to radians:
theta (in radians) = theta (in degrees) * (pi/180)
theta (in radians) = 38 * (pi/180)
theta (in radians) ≈ 0.6632 radians
Now, we can substitute the values into the formula:
F = (0.50 A) * (0.30 m) * (0.5 * 10^(-4) T) * sin(0.6632 radians)
Calculating the sin(0.6632 radians), we find:
F = (0.50 A) * (0.30 m) * (0.5 * 10^(-4) T) * 0.6147
Simplifying the expression:
F ≈ 4.61 * 10^(-6) N
Therefore, the size of the magnetic force on the wire due to the Earth's magnetic field is approximately 4.61 * 10^(-6) N.
To find the size of the magnetic force on the wire due to Earth's magnetic field, we can use the formula for magnetic force:
F = I * L * B * sin(theta)
F: Magnetic force
I: Current flowing through the wire
L: Length of the wire
B: Magnetic field strength
theta: Angle between the wire and the magnetic field
Given:
I = 0.50 A (current)
L = 0.30 m (length of the wire)
B = 0.5 x 10^-4 Tesla (magnetic field strength)
theta = 38 degrees (angle between the wire and the magnetic field)
First, we need to convert the angle theta from degrees to radians:
theta = 38 degrees = 38 * pi / 180 radians
Now, let's substitute the values into the formula:
F = (0.50 A) * (0.30 m) * (0.5 x 10^-4 Tesla) * sin(38 * pi / 180)
Calculating this expression will give us the size of the magnetic force on the wire due to Earth's magnetic field.