A conducting bar slides without friction on two parallel horizontal rails that are 50 cm apart and
connected by a wire at one end. The resistance of the bar and the rails is constant and equal to 0.10
. A uniform magnetic field is perpendicular to the plane of the rails. A 0.080-N force parallel to
the rails is required to keep the bar moving at a constant speed of 0.50 m/s. What is the magnitude
of the magnetic field?
200.0 mL of 0.750 M calcium nitrate is added to 100.0 mL of 0.500 M ammonium sulfate. What is the mass
in grams of precipitate formed?
To find the magnitude of the magnetic field, we can use the formula for the force on a current-carrying conductor in a magnetic field:
F = BIL
where F is the force, B is the magnetic field, I is the current, and L is the length of the conductor.
In this case, the force required to keep the bar moving at a constant speed is given as 0.080 N. The current (I) can be calculated using Ohm's Law:
I = V/R
where V is the voltage and R is the resistance. In this case, the voltage can be calculated using the formula:
V = Fd
where d is the distance between the rails (50 cm = 0.50 m).
First, let's calculate the current:
I = V/R = (F * d) / R = (0.080 N * 0.50 m) / 0.10 Ω = 0.40 A
Now, we can rearrange the formula for force to solve for the magnetic field (B):
B = F / (IL)
Substituting the given values:
B = (0.080 N) / ((0.40 A) * (0.50 m))
B = 0.080 N / (0.20 A * 0.50 m)
B = 0.80 T
Therefore, the magnitude of the magnetic field is 0.80 Tesla.
To find the magnitude of the magnetic field, we can use the equation for the force experienced by a moving charge in a magnetic field:
F = BIL
where F is the force, B is the magnetic field strength, I is the current, and L is the length of the conductor.
In this case, the force required to keep the bar moving at a constant speed is given as 0.080 N. The current can be calculated using Ohm's Law:
I = V/R
where V is the voltage and R is the resistance. Since the resistance is given as 0.10 Ω and the voltage is not provided, we can assume it is the same as the voltage across the resistance, which is equal to the voltage across the conducting bar.
The voltage across the bar can be calculated using the formula:
V = Fd
where d is the distance between the two rails. In this case, d is given as 50 cm, which is equal to 0.50 m.
Substituting the given values, we have:
V = 0.080 N * 0.50 m
Now we can substitute the voltage and resistance values into Ohm's Law to find the current:
I = V/R = (0.080 N * 0.50 m) / 0.10 Ω
Finally, we can substitute the values of the force, current, and length into the equation for the force experienced in a magnetic field to solve for the magnetic field strength:
F = BIL
Solving for B:
B = F / (IL)
Substituting the values, we have:
B = 0.080 N / [(0.10 Ω) * I * L]
Now we can substitute the known values to find the magnitude of the magnetic field.