Determine the strength of the current that flows through a conductor with a mass of 8 kg and a length of 20 cm

Determine the strength of the current that flows through a conductor with a mass of 8 kg and a length of 20 cm if the conductor is located horizontally in a magnetic field with an induction of 80 mT, and the force of gravity is balanced by the Ampere force.

m = 8 kg.

g = 9.8 m / s2.

L = 20cm = 0.2m.

B = 80 mT = 80 * 10-3 T.

∠α = 90 °.

I -?

Let us write down the equilibrium condition for the conductor: Ft = Famp, where Ft is the force of gravity, Famp is the Ampere force.

The force of gravity Ft is determined by the formula: Ft = m * g, where m is the mass of the body, g is the acceleration of gravity.

Ampere force Famp is determined by the formula: Famp = I * B * L * sinα, where I is the current in the conductor, B is the magnetic induction, L is the length of the conductor, ∠α is the angle between the direction of the current in the conductor and the magnetic induction B.

m * g = I * B * L * sinα.

I = m * g / B * L * sinα.

I = 8 kg * 9.8 m / s2 / 80 * 10-3 T * 0.2 m * sin90 ° = 4900 A.

Answer: the current in the conductor is I = 4900 A.