Question

an electric field E=10j exists in a space taking potential at point P(1,2,1) is zero,the electric potential at the origin will be​

Answer 1

electric field , E = 10j

potential at point P(1,2,1) is zero. i.e., $V_{(1,2,1)}=0$

we have to find potential at the origin.

using formula,

$V_{(1,2,1)}-V_{(0,0,0)}=-\int\limits^{(1,2,1)}_{(0,0,0)}\vec{E}.\vec{dr}$

Let us consider that $\vec{dr}=dx\hat{i}+dy\hat{j}+dz\hat{k}$

now, $V_{(1,2,1)}-V_{(0,0,0)}=-\int\limits^{(1,2,1)}_{(0,0,0)}\{10\hat{j}\}.\{dx\hat{i}+dy\hat{j}+dz\hat{k}\}$

or, $-V_{(0,0,0)}=-\int\limits^2_0{10}\,dy$

or, $V_{(0,0,0)}=10[2-0]=20$

hence, potential at the origin is 20 volts