Suppose that the magnetic field in the figure below has a magnitude of 1.1 T, the rod has a length of 0.86 m, and the hand keeps the rod moving to the right at a constant speed of 3.4 m/s. If the current in the circuit is 0.044 A, what is the average power being delivered to the circuit by the hand?
Answer in W
To find the average power being delivered to the circuit by the hand, we first need to understand the relationship between power (P), current (I), and voltage (V). In an electrical circuit, the formula for power is given by:
P = I * V
where P is the power in watts (W), I is the current in amperes (A), and V is the voltage in volts (V).
In this case, the current in the circuit is given as 0.044 A. However, we don't have the voltage directly. To find the voltage, we can use the formula for the electromagnetic force on a moving charge, which is given by:
F = B * I * L
where F is the electromagnetic force in newtons, B is the magnetic field strength in teslas, I is the current in amperes, and L is the length of the rod in meters.
The electromagnetic force can also be written as:
F = q * v * B
where F is the electromagnetic force in newtons, q is the charge in coulombs, v is the velocity of the charge in meters per second, and B is the magnetic field strength in teslas.
Since the hand keeps the rod moving to the right at a constant speed of 3.4 m/s, we can assume that the charges inside the rod are moving with the same velocity. Therefore, we can equate the formulas for the electromagnetic force to find the charge:
B * I * L = q * v * B
Simplifying, we find:
I * L = q * v
Now, we can substitute the given values into the equation:
0.044 A * 0.86 m = q * 3.4 m/s
Solving for q, we get:
q = (0.044 A * 0.86 m) / 3.4 m/s
q ≈ 0.01114 C
Finally, we can calculate the voltage (V) using the formula:
V = P / I
Rearranging the formula and substituting the given average power (P) and current (I), we get:
V = P / I
P = V * I
By substituting the known values, we get:
P = (q * v * B) * I
Now, we can plug in the values:
P = (0.01114 C * 3.4 m/s * 1.1 T) * 0.044 A
Solving the equation, we find:
P ≈ 0.017 W
Therefore, the average power being delivered to the circuit by the hand is approximately 0.017 watts (W).