Question

# An electron and a proton enter a magnetic field perpendicularly, both have same kinetic energy. Which of the following statements are true?

A
Trajectory of proton is less curved
B
Trajectory of electron is less curved
C
Both trajectories are equally curved
D
Both move on straight line path

Solution

## The correct option is B Trajectory of electron is less curvedWhen a charged particle enters a magnetic field perpendicularly, it moves on a circular path. The required centripetal force is provided by the magnetic force.i.e., Magnetic force $$=$$ Centripetal force$$\Rightarrow qvB=\dfrac { m{ v }^{ 2 } }{ r }$$                ....(i)Now, kinetic energy of the particle$$k=\dfrac { 1 }{ 2 } m{ v }^{ 2 }$$$$\Rightarrow mv=\sqrt { 2mk }$$Therefore, equation (i) becomes$$r=\dfrac { \sqrt { 2mk } }{ qB } \Rightarrow \dfrac { { r }_{ e } }{ { r }_{ p } } =\sqrt { \dfrac { { m }_{ e } }{ { m }_{ p } } }$$As, $${ m }_{ e } < { m }_{ p }$$; so, $${ r }_{ e } < { r }_{ p }$$Hence, trajectory of electron is less curved.Physics

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