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

Options

A. `(1.4 hat(i)-2.6 hat(j))kNC^(-1)`
B. `(1.4 hat(i)+2.6 hat(j))kNC^(-1)`
C. `(2.7hat(i)-3.6 hat(j))kNC^(-1)`
D. `(2.7 hat(i)+3.6 hat(j))kNC^(-1)`

Answer

C

Explanation

As `vec(E )=(1)/(4 pi epsilon_(0)) (q)/(|vec(r )-vec(r_0)|)(vec(r )-vec(r_0))`.

`vec(MN)=vec(r )-vecr_(0)=(8hat(i)-5 hat(j))-(2hat(i)-3hat(j))`
`=(6hat(i)-8 hat(j))`
`|vec(r )-vec(r_0)|=sqrt(6^(2)+8^(2))=10m`
`vec(E )=9xx10^(9)xx(50xx10^(-6))/((10)^(3))(6hat(i)-8hat(j))`
`=(2.7hat(i)-3.6hat(j))kNC^(-1)`.