A straight, nonconducting plastic wire 9.00 cm long carries a charge density of

Question

A straight, nonconducting plastic wire 9.00 cm long carries a charge density of 100 nC/m distributed uniformly along its length. It is lying on a horizontal tabletop Part A Find the magnitude and direction of the electric field this wire produces at a point 4.00 cm directly above its midpoint. Part B If the wire is now bent into a circle lying flat on the table, find the magnitude and direction of the electric field it produces at a point 4.00 cm directly above its center. both answers should be in N/C

Explanation / Answer

part A:

electric field on the perpendicular bisector is given by E=k*lambda*l/(y*sqrt(y^2+(l/2)^2))

where k=coloumb's constant=9*10^9

lambda=charge density=100 nC/m=10^(-7) C/m

l=length of the rod=0.09 m

y=distance from the center of the rod=0.04 m

so electric field magnitude =3.3633*10^4 N/C

field is directed along the vertical direction .

part B:

field on the axis of a uniformly charged ring is given by E=k*Q*z/(R^2+z^2)^1.5

here Q=100 nC/m * 9 cm=9 nC

z=0.04 m

if radius of the circle is R, then circumference=length of the wire

so 2*pi*R=0.09

==>R=0.014324 m

so electric field magnitude=k*Q*z/(R^2+z^2)^1.5=4.2244*10^4 N/C

field is directed in the vertically upward direction.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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