A proton enters a region of uniform magnetic field of magnitude

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A proton enters a region of uniform magnetic field of magnitude 5.0 mT5.0\,\text{mT}. The velocity of the proton makes an angle of 40∘40^{\circ} with the direction of the field. (i) Calculate the magnitude of the magnetic force acting on the proton if its speed is 2.0×106 m s−12.0\times10^{6}\,\text{m\,s}^{-1}. (ii) The proton now enters the same field at the same angle but with its speed reduced to one-half of the original value. Find the new magnitude of the force. (iii) If, instead of changing the speed, the proton were to enter the field at 90∘90^{\circ} while maintaining the original speed of 2.0×106 m s−12.0\times10^{6}\,\text{m\,s}^{-1}, by what factor would the force calculated in part (i) change? Justify your answer briefly.

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