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(B) Concept: Photoelectric effect and the motion of a charge in a direction perpendicular to a magnetic field.According to Einstein's photoelectric eq

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$\frac{\sqrt{2(E-W_0) m}}{e B}$

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(B) Concept: Photoelectric effect and the motion of a charge in a direction perpendicular to a magnetic field.According to Einstein's photoelectric equation,the maximum kinetic energy $K$ of a photoelectron is given by:$K = E - W_0$Since $K = \frac{1}{2} m v^2$,we have:$v = \sqrt{\frac{2(E - W_0)}{m}}$When a charge $e$ moves with velocity $v$ perpendicular to a magnetic field $B$,it experiences a magnetic Lorentz force that acts as a centripetal force,causing it to move in a circular path of radius $r$:$e v B = \frac{m v^2}{r}$Solving for $r$:$r = \frac{m v}{e B}$Substituting the expression for $v$:$r = \frac{m}{e B} \sqrt{\frac{2(E - W_0)}{m}} = \frac{\sqrt{m^2 \cdot \frac{2(E - W_0)}{m}}}{e B} = \frac{\sqrt{2m(E - W_0)}}{e B}$

$A$ photon of energy $E$ ejects photoelectrons from a metal surface whose work function is $W_0$. If this electron enters into a uniform magnetic field with induction $B$ in a direction perpendicular to the field and describes a circular path of radius $r$,then the radius is given by

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