A thin rod of length ell and uniform charge per unit length lambda lies along th

Question

A thin rod of length ell and uniform charge per unit length lambda lies along the x axis as shown in the figure below. (a) Show that the electric field at P_i, a distance d from the rod along its perpendicular bisector, has no x component and is given by E = 2k_e lambda sin(theta_0)/d. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Using your result to part (a), show that the field of a rod of infinite length is E = 2k_elambda/d. (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

(a)
   from the diagram we can see that the electric field atpoint P due to each element of length dx will
   be
   dE = ke dq / (x2 +y2)
   the direction is along the line joining the element topoint B
   so by symmetry we get
   Ex = d Ex
       = 0
   but as dq = dx
   from the diagram
   cos = y / (x2 +y2)
   so we get
   E = Ey
      = d Ey
      = dE cos
      = 2 ke y0(l/2) dx / (x2 +y2)3/2
      = 2 ke sino / y
(b)
   for a bar of infinite length we get
   o = 90o
   then we get
   Ey = 2 ke / y

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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