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An electron gun is emitting electrons of various speed in a region of uniform magnetic field (parallel to OP) as shown in figure. Which electrons will hit point P?

A
An electron with speed eBd6 π m cos θ
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B
An electron with speed eBdπ m cos θ
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C
An electron with energy e2B2d2π2 m cos2 θ
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D
An electron with momentum eBd4 π cos θ
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Solution

The correct options are
A An electron with speed eBd6 π m cos θ
C An electron with energy e2B2d2π2 m cos2 θ
D An electron with momentum eBd4 π cos θ

Path of electron will be helix.
Time period will be
T=2πmqB
Condition for electron to hit P is v cos θ=dnT
v=dqBn cos θ×2πm=deB2π n m cos θ
For n=3v=eBd6πm cos θ

For n = 2, the momentum will be : mv=eBd4π cosθ
and kinetic energy = 12mv2=e2B2d28π2m cos2θ

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