Question

DETAILS MY NOTES E = ASK YOUR TEACHER

(a) What is the magnitude of the electric field in a region where the potential is given by the expression V = ax2 + b where a = -325 V/m² and b = 125 V? (Substitute numerical values, and express your answer in terms of x. Assume SI units, but do not include units in your answer.) V/m² OSUNIPHYS1 24.4.WA.041. Additional Materials Reading
(b) What is the magnitude of the electric field at x = 6.75 m? V/m

Answer 1

The magnitude of the electric field in a region with potential V = ax^2 + b is found by the gradient of V, resulting in E(x) = 650x. At x = 6.75 m, the electric field's magnitude is computed by plugging in the value into the expression, yielding a specific numerical value.

Step-by-step explanation:

The magnitude of the electric field in a region where the potential is given by V = ax2 + b can be found by taking the negative gradient of the potential. Given that a = -325 V/m2 and b = 125 V, the expression for the electric field as a function of x can be derived as E = -dV/dx = -2ax. Substituting the values we have: E(x) = -2(-325)x = 650x V/m.

For the magnitude of the electric field at x = 6.75 m, we simply plug this value into the expression for E(x), yielding E(6.75) = 650 * 6.75 V/m, which is the numerical value requested for part (b).