The figure above shows a top view of a bar that can slide without friction. The resistor is 6.00 Ω and
a 2.50 T magnetic field is directed perpendicularly downward, into the paper. Let l=1.20 m.
a. Calculate the applied force required to move the bar to the right at a constant speed of 2.00 m/s.
b. At what rate is energy delivered to the resistor?
To calculate the applied force required to move the bar to the right at a constant speed of 2.00 m/s, we can use the equation:
F = BIL
Where:
F is the force applied,
B is the magnetic field strength,
I is the current flowing through the resistor, and
L is the length of the bar.
Given:
B = 2.50 T (Tesla),
R = 6.00 Ω (Ohm),
v = 2.00 m/s (velocity of the bar), and
l = 1.20 m (length of the bar).
To find the current (I), we can use Ohm's Law:
V = IR
Where:
V is the voltage across the resistor.
Since the bar is moving at a constant speed, there is no net voltage change across the resistor. Therefore, the voltage across the resistor is zero.
Now, we can calculate the applied force (F).
a. Calculate the applied force required to move the bar:
Since the applied force is equal to the magnetic force, we can use the equation:
F = BIL
Given:
B = 2.50 T,
l = 1.20 m, and
I = 0 A (since V = 0 V).
Using the formula, we have:
F = (2.50 T)(0 A)(1.20 m)
F = 0 N
Therefore, the applied force required to move the bar at a constant speed of 2.00 m/s is 0 N.
b. To calculate the rate at which energy is delivered to the resistor:
Power (P) is the rate at which energy is delivered or used:
P = IV
From part a, we know that I = 0 A. Thus, the current passing through the resistor is zero.
Given:
V = IR = 0 V
Therefore, the rate at which energy is delivered to the resistor is 0 W (watts) as well.
In summary,
a. The applied force required to move the bar at a constant speed of 2.00 m/s is 0 N.
b. The rate at which energy is delivered to the resistor is 0 W.