A proton is projected from the origin making an angle of $$60$$° with the $$x-axis$$. A magnetic field B→$$=2i^$$ tesla exists in that region of space. The proton passes through the $$x-axis$$ for the first time at a distance of $$50$$ cm from the origin. When an α $$-$$ particle is projected from the origin with same speed making an angle of $$30$$° with the $$x-axis$$ in the same magnetic field, it passes though the $$x-axis$$ at a distance ‘d’ from the origin. Then the value of ‘d’ is

Question

A proton is projected from the origin making an angle of $$60$$° with the $$x-axis$$. A magnetic field B→$$=2i^$$ tesla exists in that region of space. The proton passes through the $$x-axis$$ for the first time at a distance of $$50$$ cm from the origin. When an α $$-$$ particle is projected from the origin with same speed making an angle of $$30$$° with the $$x-axis$$ in the same magnetic field, it passes though the $$x-axis$$ at a distance ‘d’ from the origin. Then the value of ‘d’ is

Infinity Learn · Accepted Answer

Trajectory of the proton or α $$-$$ particle is helix whose pitch is given by $$p=2$$$$π$$mVcosαQB∴pα$$pp=m$$αmp QpQα $$($$$$cos$$ α$$)$$α$$($$$$cos$$ α$$)p$$⇒$$d50=(4)12cos$$ $$300cos$$ $$60o$$ ⇒d $$=$$ $$1003$$ cm

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