The potential difference between two points A(2,1,0) m and B(0,2,4) m in an electric field (x i -2 y j +z k ) Vm ⁻¹ is

Step-by-step solution

Given, electric field E =(x i -2 y i +z k ) Vm ⁻¹ Now, electric potential difference between two points A(2,1,0) and B(0,2,4) is given as aligned & V=- E d r & or - (x i -2 y j +z k )(d x i +d y j +d z k ) & =- ₂^0 x d x+2 ₁^2 y d y- ₀^4 z d z & [ -x^2 2 ]₂^0+ [y^2 ]^2- [ z^2 2 ]₀^4 & -1 2 (0^2-2^2 )+ (2^2-1^2 )- 1 2 (4^2-0^2 ) & aligned gathered - 1 2 (-4)+(4-1)- 1 2 (16)=+2+3-8 V=-3 ~V or | V|=3 ~V gathered