Imagine that new and extraordinarily precise measurements have revealed an error in Coulomb's law. The actual force of interaction between two point charges is found to be F= 1 9192 Απερ 22 + e-(2/2), where A is a new constant of nature (it has dimensions of length, obviously, and is a huge number-say half the radius of the known universe-so that the correction is small, which is why no one ever noticed the discrepancy before). You are charge with the task of reformulating electrostatics to accommodate the new discovery. Assume the principle of superposition still holds.. (a) What is the electric field of a charge distribution p (replacing Eq. 2.8)? (b) Does this electric field admit a scalar potential? Explain briefly how you reached your conclusion. (No formal proof necessary-just a persuasive argument.) (c) Find the potential of a point charge q the analog to Eq. 2.26. (If your answer to (b) was "no," better go back and change it!) Use as your reference point. (d) For a point charge q at the origin, show that ၊ E-da+ 1 22 1 V dt = 9. where S is the surface, V the volume, of any sphere centered at q. (e) Show that this result generalizes: $ E-da+ 22 L V dt = Qenc