A thin straight wire carries a current of 10 mA and makes an angle of 60° with a constant magnetic field of magnitude 10^-6 T. The portion of the wire in this field has a length of 10 cm. Calculate the magnitude of the force on this segment of the wire
The force on a current-carrying wire in a magnetic field can be calculated using the equation:
F = I * L * B * sin(θ)
Where:
F = force on the wire (in Newtons)
I = current flowing through the wire (in Amperes)
L = length of the wire segment in the magnetic field (in meters)
B = magnetic field strength (in Tesla)
θ = angle between the wire and the magnetic field (in degrees)
In this case, the given values are:
I = 10 mA = 10 * 10^-3 A = 0.01 A
L = 10 cm = 10 * 10^-2 m = 0.1 m
B = 10^-6 T
θ = 60°
Substituting these values into the equation, we have:
F = 0.01 A * 0.1 m * 10^-6 T * sin(60°)
First, let's convert the angle from degrees to radians:
θ = 60° * π/180 = π/3 radians
Now we can substitute this into the equation:
F = 0.01 A * 0.1 m * 10^-6 T * sin(π/3)
Calculating the value of sin(π/3) gives us:
F = 0.01 A * 0.1 m * 10^-6 T * (√3/2)
Simplifying further:
F = 0.01 * 0.1 * 10^-6 * (√3/2) * A * m * T
F = √3 * 10^-9 A * m * T
Finally, substituting the values:
F = √3 * 10^-9 * 0.01 * 0.1 Newtons
F ≈ 1.732 * 10^-12 Newtons
Therefore, the magnitude of the force on this segment of the wire is approximately 1.732 * 10^-12 Newtons.