Question

A wire of negligible resistance is bent into a rectangle, and a battery and resistor are connected as shown. The right-hand of the circuit extends into a region containing a uniform 38 mT magnetic field pointing into the page. Find the magnitude and direction of the net force on the circuit given that the horizontal sections of the wire that are in the magnetic field are 4 cm long and the vertical section is 5 cm long.

Answer 1

Strength of Magnetic Field, $(B)=38\space mT$

Current in the circuit, $(I)=\dfrac{V}{R}\space$

Force on section PQ of the wire = $F_{PQ}$

Force on section RS of the wire = $F_{RS}$

By symmetry, $F_{PQ}=F_{RS}$

$\therefore$ Sum of forces in vertical direction is equal to zero

Force on section QR of the wire = $F_{QR}=BILsin\theta\\$

$\theta=90\degree$ as the magnetic field is perpendicular to the direction of flow of current

$\Rightarrow F_{QR}=38\times10^{-3}\times I\times5\times10^{-2}$

Since the values of resistance and potential of the battery has not been provided

hence the value of current cannot be determined

$\therefore\space F_{QR}=19\times10^{-5}I\space N\space(towards\space right)$