Question

A wire is lying horizontally in the north-south direction and there is a horizontal magnetic field pointing towards the east. Some positive charges in the wire move north and an equal number of negative charges move south. The direction of force on the wire will be:
A. East
B. Down into the page
C. Up out of the page
D. West

Answer 1

Hint:Let us consider the coordinator axes. The direction of current the wire is along the y axis in the direction of magnetic field is along x axis. Force on the wire is given by the formula \[F = l(i \times B)\]. The direction of forces down into the page (in the direction of$({j^ \wedge } \times {i^ \wedge } = - {k^ \wedge })$

Complete answer:
Given the direction of motion of charge, the negative charge is towards the south. Current flows in the direction of motion of electric charge. Lastly, consider the directions given in the coordinate axes. The direction of the current is along the y axis(along motion of negative charge). Direction of the magnetic field is along the x axis. We know that the force on a current carrying wire is given as,
\[F = l(i \times B)\]
where $l$ is the length of the wire i is the current the wires and b is the magnetic field.

Cross product of y axis and x axis is the negative z axis
$({j^ \wedge } \times {i^ \wedge } = - {k^ \wedge })$
Therefore the direction of force on the wire is down, into the page.

Hence,option B is the correct answer.

Note:We can also find direction of force exerted on the current carrying wire using the right hand palm rule. It states that if we stretch our right hand in such a way that thumb and rest of the fingers are mutually perpendicular, and fingers show the direction of magnetic field lines, thumb shows the direction of current, then a perpendicular on the palm will show the direction of force on current carrying wire.