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  4. A very long straight wire carries a current l. At the instant when a charge +Q at point P has velocity vecv, as shown, the force on the charge is

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

AIPMTAIPMT 2005Moving Charges and Magnetism

Solution:

According to Fleming's left hand rule direction of force is along Oy axis which is perpendicular to wire.
image
$\vec{F} = e(\vec{v} \times \vec{B})$.
$B$ 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 ] $
$\therefore \vec{ F} = +Q v B \hat{j}$.
i.e in Oy direction.