Two positrons (e+) and two protons (p) are kept on four corners of a square of side a as shown in figure. The mass of proton is much larger than the mass of positron. Let q denotes the charge on the proton as well as the position then the kinetic energies of one of the positrons and one of the protons respectively after a very long time will be-

Options

A. `q^(2)/(4pi in_(0)a)(1+1/(2sqrt(2))), q^(2)/(4pi in_(0)a)(1+1/(2sqrt(2)))`
B. `q^(2)/(2pi in_(0)a),q^(2)/(4sqrt(2)pi in_(0)a)`
C. `q^(2)/(4pi in_(0)a),q^(2)/(4pi in_(0)a)`
D. `q^(2)/(2pi in_(0)a)(1+1/(4sqrt(2))), q^(2)/(8sqrt(2) pi in_(0)a)`

Answer

D

Explanation

As mass of proton `gt gt gt` mass of position so initial accelaration of position is much larger than proton. Therefore position reach far away in very short time as compare to proton.

`2K_(e^(+))=((4kq^(2))/a+(2kq^(2))/(asqrt(2)))-(kq^(2))/(asqrt(2))rArrK_(e^(+))=q^(2)/(2pi in_(0)a)(1+1/(4sqrt(2)))` and `2K_(p)=(kq^(2))/(asqrt(2))-0rArr K_(p)=q^(2)/(8sqrt(2)pi in_(0)a)`