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

Options

A. 2V
B. 3V
C. 1V
D. 6V

Answer

B

Explanation

Given, electric field E = `(x hat(i) - 2 y hat(i) + z hat(k)) V m^(-1)`
Now, electric potential difference between two points A(2,1,0) and B(0,2 ,4) is given as
`therefore " " Delta V = - int E . Dr `
Or - `int ( x hat(i) - 2 y hat(j) + z hat(k) ) (d x hat(i) + d y hat(j) + d z hat(k) ) `
= ` - int_(z)^(0) xx dx + 2 int_(1)^(2) y dy - int_(0)^(4) z dz`
`rArr " " [ (-x^(2))/(2) ]_(2)^(0) + [ y^(2) ]^(2) - [ (z^(2))/(2) ]_(0)^(4)`
`rArr " " (-1)/(2) (0^(2) - 2^(2)) + (2^(2) - 1^(2)) - (1)/(2) (4^(2) - 0^(2))`
`rArr " " - (1)/(2) (-4) + (4 -1) - (1)/(2) (16) = + 2 + 3 - 8 `
`Delta v = - 3 V or | Delta V| = 3 `V