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QJEEM19Ph700a: JEE Main 2019 Physics - Class 12 JEEM19Ph700a Solution: A positive point charge is released from rest at a distance r 0 …

A positive point charge is released from rest at a distance r0 from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :- JEE Main 2019 (Online) 8th April Evening Slot Physics - Electrostatics Question 173 English

Multiple Choice Options

  • A v∝(rr0)v \propto \left( {{r \over {{r_0}}}} \right)
  • B v∝ln⁡(rr0)v \propto \ln \left( {{r \over {{r_0}}}} \right)
  • C v∝e+r/r0v \propto {e^{ + r/{r_0}}}
  • D v∝ln⁡(rr0)v \propto \sqrt {\ln \left( {{r \over {{r_0}}}} \right)}

Step-by-Step Verified Solution

12mV2=−q(Vf−Vi){1 \over 2}m{V^2} = - q\left( {{V_f} - {V_i}} \right)

E=λ2πε0rE = {\lambda \over {2\pi {\varepsilon _0}r}}

ΔV=λ2πε0ln⁡(r0r)\Delta V = {\lambda \over {2\pi {\varepsilon _0}}}\ln \left( {{{{r_0}} \over r}} \right)

12mv2=−qλ2πε0ln⁡(r0r){1 \over 2}m{v^2} = {{ - q\lambda } \over {2\pi {\varepsilon _0}}}\ln \left( {{{{r_0}} \over r}} \right)

v∝ln⁡(rr0)v \propto \sqrt {\ln \left( {{r \over {{r_0}}}} \right)}

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