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The electric field due to electric potential V=2x24x 

(A)  (4x+4) i

(B) (4x4) i

(C) (4x+4) i

(D) (4x4) i

Answer
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Hint: The electric field at a point is defined as the negative of gradient of the potential at that point, where gradient is the dot product of Del operator with quantity V. Since only the x - component is here we get the final answer with unit vector i^.


Complete step-by-step answer:

As we know that,

E=.V= (dVdxi^+dVdyj^+dVdzk^)

This means that change in potential of a point with respect to the distance in 3 axes is termed as electric field. The negative sign is present to show that the potential of a point decreases with distance which will create a negative potential gradient.

Solving the above equation we obtain:

E= d(2x24x)dxi^

E= (4x  4)i^

E=( 4x + 4) i^

As the expression of electric field is only dependent on x, i.e. the coordinate in the i^ direction, we will add the unit vectori^ to denote the direction of the Electric field.


Therefore, the correct answer is option C.


Note: The potential and potential difference of a point is a scalar quantity but electric field is a vector quantity. An electric field is a vector quantity equal to the negative of the potential gradient. E=dVdr