A flat circular coil of turns and radius has resistance and is connected to a battery…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetostatics

Electricity, Magnetism and Electromagnetism, Ch The Biot-Savart law and the fields of steady currents

Problem

A flat circular coil of

20

turns and radius

12\,\mathrm{cm}

has resistance

2.5\,\Omega

and is connected to a battery of emf

6.0\,\mathrm{V}

and internal resistance

0.50\,\Omega

. The connecting leads have negligible resistance, the turns are close together so that all

20

may be treated as circles of the stated radius, and the current is steady. A proton passes through the point on the coil's axis a distance

16\,\mathrm{cm}

from the centre of the coil, moving at

4.0\times10^{5}\,\mathrm{m\,s^{-1}}

in a direction perpendicular to the axis. Gravity is ignored. ((a)) Find the current in the coil. ((b)) Find the magnetic field on the axis at that point. ((c)) Find the magnitude of the magnetic force on the proton there. ((d)) A thin ring of radius

12\,\mathrm{cm}

, coplanar and concentric with the coil, carries a uniformly distributed charge

Q

. What value of

Q

would make the electric force it exerts on the proton at that same axial point equal in magnitude to the answer to part (c)?

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