Question

. Electric potential at any point x, y, z in the space is
given V=4x2-3x. Find the electric field at any point (x, y, z)
(a) (8x - 3)i
(b) -(8x - 3)i
(c)-8xi
(d) 8xi​

Answer 1

Answer:

gundulodu koli the have half kshaja

Answer 2

Answer:

The electric field at any point (x, y, z) is  $-(8x-3)\hat i$.

Step-by-step explanation:

Given the electric potential at a point x, y, z in the space is $V=4x^2-3x$

Electric field is defined as the negative of the gradient of the potential.

Which can be written as

$\vec E=-\nabla \vec V$

Where the negative sign says that electric field approaches from positive charge to negative charge, the electric potential decreases.

Expanding the gradient operator in space coordinates

$\vec E=-\dfrac{d\vec V}{d\vec r} =-\bigg(\dfrac{d V}{d x}\hat i+\dfrac{d V}{d y}\hat j+\dfrac{d V}{d z}\hat k\bigg)$

Substituting the given potential, which has only the x - component,

electric field at any point (x, y, z) is

$\vec E}=-\bigg(\dfrac{d (4x^2-3x)}{dx}+0+0\bigg)$

   $=-(8x-3)\hat i$

Thus, the electric field at any point (x, y, z) is  $-(8x-3)\hat i$.

So, the correct answer is option b.

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