Magnetic Effects & Magnetism

JEE Main level, single correct, medium

135 of 276

Question 135 of 276

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6:56:5 and their respective masses ratio is 9:49:4. Then, the ratio of their charges will be

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Answer: (B) 5:45:4

Radius of charged particle moving in circular path R=2mKqBR=\dfrac{\sqrt{2mK}}{qB}, here, BB is magnetic field and KK is kinetic energy.
So, q=2mKRBq=\dfrac{\sqrt{2mK}}{RB}
Now, ratio of the charges is q1q2=m1m2×R2R1=94×56=54\dfrac{{q}_{1}}{{q}_{2}}=\sqrt{\dfrac{{m}_{1}}{{m}_{2}}}\times \dfrac{{R}_{2}}{{R}_{1}}=\sqrt{\dfrac{9}{4}}\times \dfrac{5}{6}=\dfrac{5}{4}

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