A particle of mass m and charge +q is projected with speed v from point P towards an infinite line charge, starting at distance a. Its speed becomes zero at point Q, at distance a/2 from the line. Another particle of mass m and charge −q is projected from P with the same initial speed v. Its speed at Q is Nv/√2. Find N.
Physics · Electrostatic
JEE Mains Advanced

Question

A particle of mass m and charge +q is projected with speed v from point P towards an infinite line charge, starting at distance a. Its speed becomes zero at point Q, at distance a/2 from the line. Another particle of mass m and charge −q is projected from P with the same initial speed v. Its speed at Q is Nv/√2. Find N.

Physics · Electrostatic

G1 Physics · Accepted Answer

Step 1: For +q, the particle stops at Q, so its initial kinetic energy equals the increase in electrostatic potential energy: ΔU=½mv². Step 2: For −q, the potential-energy change reverses sign, so its kinetic energy at Q is K=½mv²+½mv²=mv². Thus speed at Q is √2v. Step 3: Nv/√2=√2v gives N=2.