Question

The figure below depicts a long wire carrying a current coming out of the plane of the paper. A charge q at a distance x from it is moving towards it with speed v and experiences a magnetic force of magnitude F. If the distance of the charge from the wire were 2x (and all other conditions remaining the same) then the force would be

• A. F
• B. 2F
• C. F/2
• D. F/4

Answer 1

The correct option is C F/2

C. $\frac{F}{2}$

The magnetic field due to current carrying straight conductor at a distance $X$

$B=\frac{{\mu }_{0}I}{2\pi X}$ . . . . . . . . . .(1)

Force in a magnetic field is,

$F=q(V\times B)$,

$V$ and $B$ are perpendicular to each other.

$\theta ={90}^0$

$F=qVBsin\theta =qVB$'. . . . . . . . . . . .(2)

Put equation (1) in (2), we get,

$F=\frac{{\mu }_{0}qIV}{2\pi X}$.. . . . .(3)

Now $X^{\prime }=2X$, then

$F^{\prime }=\frac{{\mu }_{0}qIV}{2\pi X^{\prime }}=\frac{{\mu }_{0}qIV}{2\pi .2X}$

$F^{\prime }=\frac{F}{2}$