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Question: A proton of mass \(1.67 \times 10 ^ { - 27 }\)kg and charge \(1.6 \times 10 ^ { - 19 }\) C is proj...

A proton of mass 1.67×10−271.67 \times 10 ^ { - 27 }kg and charge 1.6×10−191.6 \times 10 ^ { - 19 } C is projected with a speed of 2×106 m/s2 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s } at an angle of 600 to the X-axis. If a uniform magnetic field of 0.104 Tesla is applied along Y-axis, the path of proton is

A

A circle of radius = 0.2 m and time period π×10−7\pi \times 10 ^ { - 7 } s

B

A circle of radius = 0.1 m and time period 2π×10−72 \pi \times 10 ^ { - 7 } s

C

A helix of radius = 0.1 m and time period 2π×10−72 \pi \times 10 ^ { - 7 } s

D

A helix of radius = 0.2 m and time period 4π×10−74 \pi \times 10 ^ { - 7 }s

Answer

A circle of radius = 0.1 m and time period 2π×10−72 \pi \times 10 ^ { - 7 } s

Explanation

Solution

By using r=mvsin⁡θqBr = \frac { m v \sin \theta } { q B }

T=2πmqBT = \frac { 2 \pi m } { q B } =2×π×9.1×10−311.6×10−19×0.104= \frac { 2 \times \pi \times 9.1 \times 10 ^ { - 31 } } { 1.6 \times 10 ^ { - 19 } \times 0.104 }