Question

A straight, nonconducting plastic wire 9.50 cm long carries a charge density of 130 nC/m distributed uniformly along its length. It is lying on a horizontal tabletop.A) Find the magnitude and direction of the electric field this wire produces at a point 4.50 cm directly above its midpoint.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 4.50 cm directly above its center.

Answer 1

Answer:

A) E = 3.70*10^{4} N/C

B)  E = 2.281*10^3 N/C

Explanation:

given data:

charge density $\lambda = 130*10^{-9} C/m$

length of wire = 9.50 cm

a) at x  = 4.5 m above midpoint, electric field is calculated as

$E = \frac{1}{ 2\pi \epsilon} * \frac{ \lambda}{x\sqrt{(x^2/a^2)+1}}$

x = 4.5 cm

midpoint a = 4.5 cm = 0.0475 m

$E =2{\frac{1}{ 8.99*10^9} * \frac{130*10^{-9} }{0.045\sqrt{(4.5^2/4.75^2)+1}}$

E = 3.70*10^{4} N/C

B) when wire is in circle form

$Q = \lambda * L$

$= 130*10^{-9} *9.5*10^{-2}$

   = 1.235*10^{-8} C

Radius of circle

$r = \frac{L}{2\pi}$

$r = \frac{9.5*10^{-2}}{2\pi}$

r = 1.511*10^{-2} m

$E = \frac{1}{ 2\pi \epsilon} * \frac{Qx}{(x^2+r^2)^{3/2}}$

$E =8.99*10^{9} * \frac{1.23*10^{-8}*4.5*10^{-2}}{((4.5*10^{-2})^2+(1.511*10^{-2})^2)^{3/2}}$

E = 2.281*10^3 N/C