Two parallel METAL rods form a plane inclined at 20.0° to the horizontal. The upper end of the rods are connected together by a resistor of 118.0 Ω. The lower end of the rods are held in an ELECTRICALLY INSULATING block. They are separated horizontally by a distance of 20.0 cm There is a uniform magnetic field of 0.100 T DIRECTED vertically upward. A metal bar of mass 0.10 g is SLIDING down the metal rods. What is the maximum speed of the bar? Assume: no frictional loss and that the rods are very long; g=9.8 m/s2.

To find the maximum speed of the metal bar sliding down the metal rods, we need to consider the electric and magnetic forces acting on the bar.

First, let's determine the electric field between the metal rods. Since the rods are parallel and connected by a resistor, they form a simple series circuit. We can use Ohm's Law to find the current flowing through the circuit:

V = I * R,

where V is the voltage across the resistor, I is the current, and R is the resistance. In this case, the voltage across the resistor is the voltage difference between the metal rods.

The voltage difference between the metal rods can be calculated using trigonometry:

ΔV = 2 * V * sin(θ),

where V is the potential difference between the ends of the metal rods and θ is the angle between the rods and the horizontal plane (20.0° in this case).

Now, we can calculate the current:

I = ΔV / R.

Next, let's determine the magnetic force acting on the metal bar sliding down the rods. The magnetic force can be calculated using the equation:

F = B * I * L,

where B is the magnetic field strength, I is the current, and L is the length of the metal bar.

However, since the bar is sliding down the rods, we need to account for the gravitational force pulling it downward. The net force acting on the bar is given by:

F_net = F_magnetic - F_gravity.

Finally, we can calculate the maximum speed of the bar using the equation:

v = √(2 * d * a),

where d is the distance traveled and a is the acceleration. In this case, the distance traveled is the separation between the metal rods (20.0 cm) and the acceleration is the net force acting on the bar divided by its mass.

Using the given values and equations, we can find the maximum speed of the bar sliding down the metal rods.