At any point (.x,0,0.), the electric potential V is ((10/x) + (15/x2) + (5/x3)) volt, then electric field at x=1m is

Question

At any point (.x,0,0.), the electric potential V is ((10/x) + (15/x2) + (5/x3)) volt, then electric field at x=1m is (A) 55(. hatj+ hatk.)∨ /m (B) 55 hativ/m (C) (55/√2)(. hati+ hatk.)v/m (D) 55 hatjv/m

Tardigrade Admin · Accepted Answer

overset arrow E=-(dv/dx) hati =-(dV/dx)[(10/x) + (15/x2) + (5/x3)] hati =-[- (10/x2) - (30/x3) - (15/x4)] hati At x=1 overset arrow E=10+30+15 =55 hati

Q. At any point $(x, 0, 0),$ the electric potential $V$ is $(\frac{10}{x} + \frac{15}{x ^{2}} + \frac{5}{x ^{3}})$ volt, then electric field at $x = 1 m$ is

$55 (\hat{j} + \hat{k}) \lor / m$

$55 \hat{i} v / m$

$\frac{55}{2} (\hat{i} + \hat{k}) v / m$

$55 \hat{j} v / m$

$E \to = - \frac{d v}{d x} \hat{i}$
$= - \frac{d V}{d x} [\frac{10}{x} + \frac{15}{x ^{2}} + \frac{5}{x ^{3}}] \hat{i}$
$= - [- \frac{10}{x ^{2}} - \frac{30}{x ^{3}} - \frac{15}{x ^{4}}] \hat{i}$
At $x = 1$
$E \to = 10 + 30 + 15$
$= 55 \hat{i}$

Q. At any point (x,0,0), the electric potential V is (x10​+x215​+x35​) volt, then electric field at x=1m is

55(j^​+k^)∨/m

55i^v/m

2​55​(i^+k^)v/m

55j^​v/m