A metal bar with a length of 0.30 m and mass of 0.5 kg is free to slide (no friction) on a set of vertical rails. The rails and bar together have a resistance of 500 ohms. The rails lie in a horizontal magnetic field with a strength of 0.04 T. The mass falls under the combined influence of gravity and magnetic forces with a constant speed.

Magnitude of the force of gravity?
Magnitude of the magnetic force on the rod?
Current in the rod?
Direction of that current?
EMF on the rod?
Speed of the rod?

0.6

To find the magnitude of the force of gravity on the metal bar, we can use the formula F = mg, where m is the mass of the bar and g is the acceleration due to gravity. In this case, the mass of the bar is given as 0.5 kg. The acceleration due to gravity on Earth is approximately 9.8 m/s². So, we can calculate the force of gravity as follows:

F_gravity = (0.5 kg) * (9.8 m/s²) = 4.9 N

The magnitude of the magnetic force on the rod can be calculated using the formula F_magnetic = BIL, where B is the magnetic field strength, I is the current flowing through the rod, and L is the length of the rod. In this case, B is given as 0.04 T and L is given as 0.30 m. We need to find the current flowing through the rod.

To find the current in the rod, we can use Ohm's Law (V = IR), where V is the voltage across the rod and R is the resistance of the system. The resistance of the system is given as 500 ohms. The voltage across the rod is equal to the induced electromotive force (EMF) caused by the magnetic field. Since the bar is moving at a constant speed, the net force on the bar must be zero, meaning the magnetic force is equal in magnitude and opposite in direction to the force of gravity. This ensures a constant velocity.

Thus, F_magnetic = F_gravity

BIL = mg

I = (mg) / (BL)

Now we can substitute the known values:

I = (0.5 kg * 9.8 m/s²) / (0.04 T * 0.30 m) = 81.67 A (rounded to two decimal places)

The direction of the current can be determined using the right-hand rule. If you point your right thumb in the direction of the magnetic field (horizontal), and your other fingers wrap around the bar in the direction of the electron flow (opposite to conventional current flow), then the direction of the current will be from your palm towards your fingers.

The EMF (voltage) on the rod will be equal to the product of the current and the resistance. So, the EMF can be calculated as:

EMF = I * R

EMF = (81.67 A) * (500 ohms) = 40835 V (rounded to two decimal places)

The speed of the rod is given as constant, which means the net force acting on it must be zero. The net force can be found by calculating the difference between the magnetic force and the force of gravity, and the net force is equal to mass times acceleration (F_net = ma). Since the metal bar moves at a constant speed, the net force is zero.

(0.04 T * I * L) - (mg) = 0

Now we can calculate the speed:

Speed = (mg) / (BIL)

Speed = (0.5 kg * 9.8 m/s²) / (0.04 T * 81.67 A * 0.30 m) ≈ 2.03 m/s (rounded to two decimal places)