Question

The magnetic field of the earth near the equator is has a value $B_E$.
A wire of length $L$ is carrying a current $I$ in such a way that the wire is suspended by the magnetic field.
In terms of $B_E.,L,m$, and fundamental constants which of the following is an expression for the current on the wire and the direction of conventional current flow?

• A. $\frac{mg}{B_{E}L}$, East
• B. $\frac{mg}{B_{E}L}$, West
• C. $\frac{g}{B_E}$, East
• D. $\frac{B_{E}L}{mg}$, East
• E. $\frac{B_{E}L}{mg}$, West

Answer 1

Answer: (A)

$\frac{mg}{B_{E}L}$, East

The direction of earth's magnetic field is from geographical south to north pole of earth , at equator earth's magnetic field is parallel to the earth's surface .

The force $F$ experienced by a conductor of length $L$ , carrying a current $I$ , placed perpendicular to magnetic field $B$ is given by ,

$F=ILB$ ,

as the wire is suspended , it means its weight $mg$ is balanced by earth's magnetic force in upward direction ,

$IL{B}_E=mg$ , ($B_E=$ earth's magnetic field) ,

or $I=mg/B_{E}L$ ,

the direction of magnetic field is from south to north and force on wire is in upward direction therefore by Fleming's left hand rule , the direction of current will be toward east .