A proton of mass 1.67×10−27 kg and charge 1.68×10−19 C is projected with a speed of 2×106ms−1 at an angle of 60o to the X−axis. If a uniform magnetic field of 0.10 T is applied along Y−axis, the path of proton is :
A
a circle of radius 0.2 m and time period π×10−7s
B
a circle of radius 0.1 m and time period 2π×10−7s
C
a helix of radius 0.1 m and time period 2π×10−7s
D
a helix of radius 0.2 m and time period 4π×10−7s
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Solution
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vx=vcosθ vy=vsinθ Since vy≠0, this component will be responsible for motion along the direction B( i.e y−axis). The path will be helical and pitch will be constant. Radius r of the circle perpendicular to the magnetic field B
A proton of mass 1.67×10−27 kg and charge 1.6×10−19 C is projected with a speed of 2×106m/s at an angle of 60∘ to the X-axis. If a uniform magnetic field of 0.104 Tesla is applied along Y-axis, the path of proton is
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Q2
A particle having a charge of 2.0×10−8 C and a mass of 2.0×10−10 g is projected with a speed of 2.0×103 m s−1 in a region having a uniform magnetic field of 0.10 T. The velocity is perpendicular to the field. Find the radius of the circle formed by the particle and also the time period.
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Q3
A proton of mass 1.67×10−27kg and charge 1.6×10−19C is projected with a speed of 2×10−6m/s at an angle of 60∘ with the X-axis. If a uniform magnetic field of 0.104T is applied along Y-axis, the path of the proton is
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Q4
A proton of charge 1.6×10−19C and mass m=1.67×10−27kg is shot with a speed 8×106m/s at an angle of 30∘with x-axis. A uniform magnetic field B=0.30T exist along the x-axis. Find the radius of the helical path followed by the proton ?
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Q5
A particle of charge 2.0 × 10−8 C and mass 2.0 × 10−10 g is projected with a speed of 2.0 × 103 m s−1 in a region with a uniform magnetic field of 0.10 T. The velocity is perpendicular to the field. Find the radius of the circle formed by the particle and also the time period.