An 8m long copper wire with a cross-sectional area of 1.0 x 10^-4 m^2, in the sshape of square loop, is connected to a .10-V battery. If the loop is placed in a uniform magnetic field of magnitude .4T, what is the maximum torque that can act on it? The resistivity of copper is 1.7x10^-8 omega*m (answer: 120 N*m) I can't seem to get the answer. Any help is appreciated!
work:
I=V/R=(.10V)/((1.7x10^-8)/8m))
torque=BIA=(.4T)(I)(10^-4 m^2)
You have not used the wire resistance R in the Ohm's law equation; you used resistivity, which must be multiplied bu L/A*, where A* is the cross sectional area of the wire (1.0 x 10^-4 m^2) and L is its total length (8 m). The area A that should go into your second equation is the coil area, (L/4)^2 = 4 m^2, since is it s square.
To find the maximum torque that can act on the copper wire loop, we can follow these steps:
1. Calculate the resistance of the copper wire:
The resistance of a wire can be calculated using the formula: R = ρ * (L / A), where ρ is the resistivity of copper (given as 1.7x10^-8 Ω*m), L is the length of the wire (given as 8m), and A is the cross-sectional area of the wire (given as 1.0x10^-4 m^2).
Substituting the given values, we get:
R = (1.7x10^-8 Ω*m) * (8m) / (1.0x10^-4 m^2)
Calculating this gives us the resistance, R.
2. Calculate the current flowing through the wire:
Since the wire is connected to a battery with a voltage of 0.10V, we can calculate the current (I) using Ohm's Law: I = V / R, where V is the voltage and R is the resistance calculated in the previous step.
Substituting the given values, we get:
I = 0.10V / R
Calculating this gives us the current, I.
3. Calculate the maximum torque:
The torque (τ) acting on a loop of wire in a magnetic field can be calculated using the formula: τ = B * I * A, where B is the magnitude of the magnetic field (given as 0.4T), I is the current flowing through the wire, and A is the cross-sectional area of the wire.
Substituting the given values, we get:
τ = (0.4T) * I * (1.0x10^-4 m^2)
Calculating this gives us the maximum torque, τ.
By following these steps, you should be able to calculate the maximum torque acting on the copper wire loop.