A copper ring made of a wire with a diameter of 4 mm is located in a uniform magnetic field, the magnetic

A copper ring made of a wire with a diameter of 4 mm is located in a uniform magnetic field, the magnetic induction of which changes in absolute value at a speed of 1.48 tesla per second. The plane of the ring is perpendicular to the vector of magnetic induction. What is the diameter of the ring if the induction current is 8 amperes.

The absolute value of the induced EMF in the ring E:

E = ΔФ / Δt,

where ΔФ is the change in magnetic flux,

Δt is the time of change.

ΔФ = S * ΔB = (пD2 * ΔB) / 4,

where S is the area covered by the ring,

ΔB – change in magnetic induction,

D is the diameter of the ring. d

E = nD2ΔB / 4Δt.

Copper ring resistance:

R = ρL / s = ρpD / (pd2 / 4) = 4ρD / d2,

where ρ is the resistivity of copper,

L = пD – wire length,

d – wire diameter.

s = пd2 / 4 – wire cross-sectional area.

Answer: 0.03 m (3 cm)