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Question:

An electron, moving along the x-axis with an initial energy of 100eV, enters a region of magnetic field B→=(1.5×10⁻³T)k^ at S (See figure). The field extends between x=0 and x=2cm. The electron is detected at the point Q on a screen placed 8cm away from the point S. The distance d between P and Q (on the screen) is :(electron's charge =1.6×10⁻¹⁹C, mass of electron =9.1×10⁻³¹kg)

12.87cm

11.65cm

1.22cm

2.25cm

Solution:

Correct option is B.
1.22cm
R=mv/qB=√(2m(K.E))/qB
R=√(2×9.1×10⁻³¹×(100×1.6×10⁻¹⁹))/(1.6×10⁻¹⁹×1.5×10⁻³)
R=2.248cm
sin θ = 2R/8
tan θ = d/8
QU/TU ≈ 2.026 = QU/8
QU = 11.69cm
PU = R(1-cos θ) = 1.22cm
d = QU + PU