What is the magnitude of the electric field in a region where the potential is given by the expression V = ax2 + b where a = −500 V/m2 and b = 135 V? (Substitute numerical values, and express your answer in terms of x. Assume SI units, but do not include units in your answer.)

The point represents the scalar product, in this case we calculate the electric field in the x-axis and the potential is also in this axis so the scalar product is reduced to the algebraic product

E = dV /dx

Let's make the derivative

E = - 2ax

Let's replace the values

E = -2 (-500) x

E = 1000 x

stigawithfun stigawithfun · Answer 2 · 2020-02-25T11:04:07+01:00

Answer:

The equation of the electric field (E) is given by;

E = -1000x

Explanation:

The electric field (E) is the gradient of the potential difference (V) in the direction of x between two points. i.e

E = [tex]\frac{dV}{dx}[/tex] ----------------------(i)

From the question;

V = ax² + b ---------------(ii)

Find the gradient of equation (ii) by taking derivative of both sides with respect to x as follows;

[tex]\frac{dV}{dx}[/tex] = [tex]\frac{d(ax^{2} + b)}{dx}[/tex]

[tex]\frac{dV}{dx}[/tex] = 2ax ----------------------(iii)

Substitute [tex]\frac{dV}{dx}[/tex] = 2ax into equation (i) as follows;

E = 2ax --------------------------(iv)

Now, substitute the value of a = -500 into equation (iv) as follows;

E = 2(-500)x

E = -1000x

Therefore, the equation of the electric field (E) is given by;

E = -1000x