Question

A very long straight wire carries a current $l$. At the instant when a charge +Q at point P has velocity $\overrightarrow{v}$, as shown, the force on the charge is

• A. along Oy
• B. opposite to Oy
• C. along Ox
• D. opposite to Ox

Answer 1

Answer: (A)

along Oy

Answer 2

According to Fleming's left hand rule direction
of force is along Oy axis which is perpendicular to wire.

$\overrightarrow{F} = e(\overrightarrow{v} \times \overrightarrow{B})$.
B due to i is acting inwards i.e. into the paper.
v is along Ox.
$\therefore \ \ F = Q^+ \begin {vmatrix} \widehat{i} & \widehat{j} & \widehat{k} \\\ v & 0 & 0 \\\ 0 & 0 & -B \end {vmatrix} \Rightarrow F = Q^+ [ - \widehat{j}(-v B)+ 0 ]$
$\therefore \overrightarrow{ F} = +Q v B \widehat{j}$.
i.e in Oy direction.