A copper wire is 7.00 m long and has a cross-sectional area of 1.00 10-4 m2. This wire forms a one turn loop in the shape of a square and is then connected to a battery that applies a potential difference of 0.200 V. If the loop is placed in a uniform magnetic field of magnitude 0.600 T, what is the maximum torque that can act on it? The resistivity of copper is 1.7 10-8 · m.
To find the maximum torque acting on the square loop, we can use the equation:
τ = N * B * A * I * sinθ
where:
τ is the torque,
N is the number of turns in the loop,
B is the magnetic field strength,
A is the area of the loop, and
I is the current flowing through the loop.
In this case, the loop has one turn (N = 1), and the area is given as 1.00 * 10^(-4) m². We need to determine the current flowing through the loop.
To calculate the current, we can use Ohm's Law:
V = I * R
where:
V is the potential difference (0.200 V) from the battery, and
R is the resistance of the wire.
The resistance can be calculated using the formula:
R = (ρ * L) / A
where:
ρ is the resistivity of copper (1.7 * 10^(-8) Ω·m),
L is the length of the wire (7.00 m), and
A is the cross-sectional area of the wire (1.00 * 10^(-4) m²).
Let's plug in the values step by step to calculate the maximum torque:
First, calculate the resistance:
R = (1.7 * 10^(-8) Ω·m * 7.00 m) / (1.00 * 10^(-4) m²)
Now, calculate the current:
I = V / R
Finally, substitute the values into the torque equation and calculate the maximum torque.