An electric charge `2 xx 10^(-8) C` is placed at the point `(1,2,4)`. At the point `(3,2,1)` , the electric
(i) potential will be `50 V`
(ii) field will have no `Y`-component
(iii) field will increase by a factor `K` if the space between the points is filled with a dielectric of constant `K`
(iv) field will be along `Y`-axis

Options

A. `(i),(ii)`
B. `(i),(iii)`
C. `(i),(iv)`
D. all

Answer

1

Explanation

Distance between `A(1 , 2, 4)` and `B(3 , 2, 1)`
`r = sqrt((3 - 1)^(2) + (2 - 2)^(2) + (1 - 4)^(2)) = sqrt(13)`
`V = (1)/(4 pi in_(0)) (Q)/(r ) = ( 9 xx 10^(9) xx 2 xx 10^(-8))/(sqrt(13))= 50` volt
`E = (1)/(4 pi in_(0)) (Q)/(r^(2)) = ( 9 xx 10^(9) xx 2 xx 10^(-8))/(13) = (180)/(13) N//C`
Unit vector along `AB , hat(r ) = (2 hat(i) - 3 hat(k))/(sqrt(13))`
`vec(E ) = E hat(r ) = (180)/(13 sqrt(13)) (2 hat(i) - 3 hat(k))`