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.)

E = 1000 x

Explanation:

The electric potential and the electric field are related by the formula

        dV = - E . dx

Bold represents vectors.

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

work: w = fd (given)

work done by chet   =50*1 = 50 j

work done by mika =40*2 = 80 j

work done by sara =30*1.5 = 45 j

work done by bill =60*0.5 = 30 j

students in order from the greatest amount of work done to the least is mika> chet> sara> bill

hence option (b) is correct.