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Question

Question: The electric potential \(V\) is given as a function of distance \(x\) (metre) by \(V = (5x^{2} + 10x...

The electric potential VV is given as a function of distance xx (metre) by V=(5x2+10x9)voltV = (5x^{2} + 10x - 9)volt. Value of electric field at x=1x = 1 is

A

20V/m20V/m

B

6V/m6V/m

C

11V/m11V/m

D

23V/m- 23V/m

Answer

20V/m20V/m

Explanation

Solution

E=dVdx=ddx(5x2+10x9)=10x10E = - \frac{dV}{dx} = - \frac{d}{dx}(5x^{2} + 10x - 9) = - 10x - 10

(E)x=1=10×110=20V/m(E)_{x = 1} = - 10 \times 1 - 10 = - 20V/m