A non-conducting charged sheet and a non-conducting sphere (radius b) are arrang

Question

A non-conducting charged sheet and a non-conducting sphere (radius b) are arranged as shown in the figure. The right-most surface of the sheet is at x = 0 and the center of the sphere is on the x-axis at x = x0. The sheet has a positive uniform charge density sigma while the sphere is uniformly charged with total negative charge - q (where q itself is positive). Answer the following questions regarding the electric field and the electrostatic potential V(x). Using proper unit-vector notation, write down the appropriate expression for at point P. Determine whether the following potential V(x) gives the correct at point P: V(x) = -sigma/ epsilon 0 x2 - kq/(x0 - x) What must V(x) be so that it gives at point P and is also zero at the surface of the plane (i. e. , V(0) = 0)? Verify your answer with an appropriate integral.

Explanation / Answer

a)

E = E1 + E2 = /(20) + kq/(x0-x)2

b)

The given potential V(x) does not give the correct E(x) at point P :

E(x) = -dV/dx = -d(-x2/4e0-kq/(x0-x))/dx = x/20 + kq//(x0-x)

c)

V(x) = x/(20) - kq/(x0-x)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.