A particle of charge Q and mass m moves in a circular path of radius R in a uniform magnetic field of magnitude B. The same particle now moves with the same speed in a circular path of same radius R in the space between the cylindrical electrodes of the cylindrical capacitor. The radius of the inner electrode is $R/2$ while that of the outer electrode is $3R/2$ . Then the potential difference between the capacitor electrodes must be

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

QBR (In3) /m

Zero

{QB}^{2} R^{2} (In3) /2m

{QB}^{2} R^{2} (In3) /m

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$F_{ER} = F_{CP}$

$\Rightarrow E_{q} = \frac{{mV}^{2}}{r}$

$R = \frac{mV}{Bq} V = \frac{BqR}{m}$

$\frac{λ Q}{2 π E_{0} R} = \frac{m}{R} {(\frac{BRQ}{m})}^{2}$

$\frac{λ}{2 π E_{0}} = \frac{B^{2} R^{2} Q}{m} \to (1)$

$dV = Edr \Rightarrow dV = \frac{λ}{2 π E_{0}} . \frac{1}{r} dr$

$V_{2} - V_{1} = \frac{λ}{2 π E_{0}} {(\ln r)}_{8 / 2}^{3R/2}$

$V_{2} - V_{1} = \frac{B^{2} R^{2} Q}{m} (\ln 3)$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE