ch22-p027 - 27(a The linear charge density is the charge...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Let dx be an infinitesimal length of rod at x . The charge in this segment is dq dx . The charge dq may be considered to be a point charge. The electric field it produces at point P has only an x component and this component is given by dE dx Lax x = +− 1 4 0 2 π ε λ bg . The total electric field produced at P by the whole rod is the integral () () () 2 0 0 00 0 00 11 1 44 4 , 44 L L x dx E Lax a La Lax Lq aL a aL a εε ε εε λλ λ ⎛⎞ == = ⎜⎟ π + ⎝⎠ +− λ1 == π+ π+ upon substituting qL λ −= . With q = 4.23 × 10 15 C, L =0.0815 m and a = 0.120 m, we obtain 3 1.57 10 N/C x E =− × , or 3 | | 1.57 10 N/C x E . (c) The negative sign in x E indicates that the field points in the – x direction, or 180 ° counterclockwise form the + x axis. (d) If a is much larger than L , the quantity L + a in the denominator can be approximated by a and the expression for the electric field becomes E q a x =− 4 0 2 π ε . Since 50 m 0.0815 m, aL == ± the above approximation applies and we have 8 1.52 10 N/C
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online