Suppose there is a uniform electric field in the (+x)direction If a negative charge moves in the (-x)direction; does - Physics - Electrostatic Potential And Capacitance

Question

Suppose there is a uniform electric field in the (+x)direction If a
negative charge moves in the (-x)direction; does the electric
potential energy increase or decrease? Explain

Ved Prakash Lakhera · Accepted Answer

The electric potential energy will incease because of following reason,Elelctric potential energy=-∫eE
dr=-14πε0×e×∫rArBqr2
drWhere e is electronic charge, q the charge of electric field E and rB<rA
On integration potential energy becomes,U=-eq4πε0×-1rrArB=eq4πε0×1rB-1rA
Since rA>rB, therefore electric potential energy is positive

Suppose there is a uniform electric field in the (+x)direction. If a negative charge moves in the (-x)direction; does the electric potential energy increase or decrease? Explain.