At any point (x , 0 , 0) the electric potential V is ((1000/x) + (1500/x2) + (500/x3)) volt , then electric field intensity at x=1 m is

Question

At any point (x , 0 , 0) the electric potential V is ((1000/x) + (1500/x2) + (500/x3)) volt , then electric field intensity at x=1 m is (A) 5500( hatj + hatk)Vm- 1 (B) 5500 hatiVm- 1 (C) (5500/√2)( hatj + hatk)Vm- 1 (D) (5500/√2)( hati + hatk)Vm- 1

Tardigrade Admin · Accepted Answer

Electric potential V=((1000/x) + (1500/x2) + (500/x3)) Electric field E=-(dV/dx)=((1000/x2) + ((2) 1500/x3) + ((3) 500/x4)) hati At x=1 , E=5500 hati Vm- 1

Q. At any point $(x, 0, 0)$ the electric potential $V$ is $(\frac{1000}{x} + \frac{1500}{x ^{2}} + \frac{500}{x ^{3}}) v o lt$ , then electric field intensity at $x = 1 m$ is

$5500 (\hat{j} + \hat{k}) V m^{- 1}$

$5500 \hat{i} V m^{- 1}$

$\frac{5500}{2} (\hat{j} + \hat{k}) V m^{- 1}$

$\frac{5500}{2} (\hat{i} + \hat{k}) V m^{- 1}$

Electric potential
$V = (\frac{1000}{x} + \frac{1500}{x ^{2}} + \frac{500}{x ^{3}})$
Electric field
$E = - \frac{d V}{d x} = (\frac{1000}{x ^{2}} + \frac{( 2 ) 1500}{x ^{3}} + \frac{( 3 ) 500}{x ^{4}}) \hat{i}$
At $x = 1$ ,
$E = 5500 \hat{i} V m^{- 1}$

Q. At any point (x,0,0) the electric potential V is (x1000​+x21500​+x3500​)volt , then electric field intensity at x=1m is

5500(j^​+k^)Vm−1

5500i^Vm−1

2​5500​(j^​+k^)Vm−1

2​5500​(i^+k^)Vm−1