An electric current I enters and leaves a uniform circular wire of radius r through diametrically opposite points. A charged particle q moves along the axis of circular wire passes through its centre with speed v . The magnetic force on the particle when it passes through the centre has a magnitude

Step-by-step solution

The circular wire is divided into two semi-circular segments by the diametrically opposite points where the current enters and leaves. Let the current I split into I₁ and I₂ through the two semi-circular paths. Since the wire is uniform, the resistance of each semi-circular path is equal, so I₁ = I₂ = I/2 . The magnetic field B₁ at the center due to the first semi-circular wire carrying current I/2 is directed perpendicular to the plane of the loop. Using the Biot-Savart law, the magnetic field at the center of a f