A positive point charge `50mu C` is located in the plane xy at a point with radius vector `vecr_(0)=2hat(i)+3hat(j)`. The electric field vector `vec(E )` at a point with radius vector `vec(r )=8 hat(i)-5 hat(j)`, where `r_(0)` and r are expressed in meter, is

Explanation

here `q= 50 xx 10^(-6)C`
`vec(r ) = (vec(r )_(2)-vec(r )_(1)) = (8 hat(i) - 5hat(j)) - (2hat(i) + 3hat(j)) = (6 hat(i) - 8hat(j))`
`bar(E )= (1)/(4pi in_(0)) (q)/(r^(3)) bar(r ) rArr (9 xx 10^(9) xx 50 xx 10^(-6))/(1000) xx (6 hat(i) - 8hat(j))` then `bar(E )= 450 (6 hat(i) - 8hat(j))NC^(-1) = 900(3 hat(i) - 4hat(j))NC^(-1)`