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JIPMER 2010
Exam
JIPMER
Year
2010
Subject
Physics
Chapter
Magnetic Effects of Current

JIPMER 2010 · Physics · Magnetic Effects of Current

An electron of mass m and charge q is travelling with a speed v...

An electron of mass mm and charge qq is travelling with a speed vv along a circular path of radius rr at right angles to a uniform magnetic field BB. If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

Options

  1. Ar4\frac{r}{4}
  2. Br2\frac{r}{2}
  3. C2r2 r
  4. D4r4 r

Correct answer

D. 4r4 r

Step-by-step solution

In a perpendicular magnetic field, Magnetic force = centripetal force ie, Bqv=mv2r⇒r=mvBq∴r1r2=v1v2×B2B1r1r2=12×12r2=4r1⇒r2=4r\begin{aligned} & B q v=\frac{m v^2}{r} \Rightarrow r=\frac{m v}{B q} \\ & \therefore \quad \frac{r_1}{r_2}=\frac{v_1}{v_2} \times \frac{B_2}{B_1} \\ & \frac{r_1}{r_2}=\frac{1}{2} \times \frac{1}{2} \\ & r_2=4 r_1 \\ & \Rightarrow \quad r_2=4 r \\ & \end{aligned}
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