A uniform magnetic field exists in a region which forms an equilateral triangle of side a. The magnetic field is perpendicular to the plane of the triangle. A charge q enters into this magnetic field perpendicular to a side with speed v.The charge enters from midpoint and leaves the field from mid-point of other side. Magnetic induction in the triangle is

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$\frac{2 m v}{q a}$

$\frac{m v}{q a}$

$\frac{m v}{4 q a}$

$\frac{m v}{2 q a}$

answer is B.

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Detailed Solution

The charged particle moves in a circle of radius a/2.

$q v B = \frac{m v^{2}}{a / 2} or B = \frac{2 m v}{q a}$

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