An H-shaped structure of thick copper rods arranged vertically is placed in a uniform horizontal

An H-shaped structure of thick copper rods arranged vertically is placed in a uniform horizontal magnetic field of induction B = 0.04 T. On the rods, a thin copper jumper slides freely from top to bottom without breaking the contact. What is the maximum speed it will reach? The resistance of all parts, except for the jumper, should be neglected (copper resistivity 1.7 * 10 ^ -2 Ohm * m, copper density 8.8 * 10 ^ 3 kg / m ^ 3).

1. To begin with, we find the strength of the current piercing through the jumper, based on the EMF:
B * v * L = I * R;
Let’s transform:
B * v = I * p / S;
Let’s transform:
I = B * v * S / p;
2. At maximum speed, the jumper moves uniformly under the action of gravity and Ampere force:
B * I * L = m * g;
Let’s transform:
B ^ 2 * v * S * L / p = p’S * L * g;
Let’s transform:
B ^ 2 * v / p = p’g;
Let’s transform:
v = p * p’g / B ^ 2;
Let’s substitute:
v = 1.7 * 10 ^ -8 * 8.8 * 10 ^ 3 * 10/16 * 10 ^ -4;
V = 0.935 m / s.
Answer: V = 0.935 m / s.