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  4. A uniform magnetic field exists in 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 perpendicularly with speed v along perpendicular bisector of one side and comes out along the perpendicular bisector of other side. The magnetic induction in the triangle is

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Q. A uniform magnetic field exists in 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 perpendicularly with speed $v$ along perpendicular bisector of one side and comes out along the perpendicular bisector of other side. The magnetic induction in the triangle is

NTA AbhyasNTA Abhyas 2020Moving Charges and Magnetism

Solution:

The charged particle moves in a circle of radius $\frac{a}{2}$
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$\therefore qvB=\frac{m v^{2}}{\frac{a}{2}}$ or $B=\frac{2 m v}{q a}$