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s A horizontal insulating rod of length 11.0-cm and charge 19 nC is in a plane with a long straight vertical uniform line charge. The linear charge density of the long line charge is 3.9x10-7 c/m. What is the electric force on the rod if the end closest to the line charge is 2.0 cm away?

Respuesta :

Answer:

F = 2.26 ×  10⁻³ N

Explanation:

given,

length of rod = 11 cm

charge  = 19 nC

linear charge density = 3.9 x 10⁻⁷ C/m

electric force at 2 cm away.

[tex]E(r) = \dfrac{2K\lambda}{r}[/tex]

F = E q

[tex]F= \dfrac{2K\lambda\ q}{L}\int \dfrac{dr}{r}[/tex]

integrating from 0.02 to 0.02 + L

[tex]F= \dfrac{2K\lambda\ q}{L}[ln(0.02+L)-ln(0.002)][/tex]

[tex]F= \dfrac{2\times 9 \times 10^9\times 3.9\times 10^{-7}\times 19 \times 10^{-9}}{0.11}[ln(0.02+0.11)-ln(0.002)][/tex]

F = 2.26 ×  10⁻³ N

okpalawalter8

We have that for the Question "What is the electric force on the rod if the end closest to the line charge is 2.0 cm away" it can be said that

  • F=2.26*10^{-3}

From the question we are told

  • A horizontal insulating rod of length 11.0-cm and charge 19 nC is in a plane with a long straight vertical uniform line charge.
  • The linear charge density of the long line charge is 3.9x10-7 c/m.
  • What is the electric force on the rod if the end closest to the line charge is 2.0 cm away?

the electric force

Generally the equation for the  the electric force  is mathematically given as

[tex]E=\frac{2k\lambda}{r}\\\\Therefore\\\\F=\frac{2k\lambdaq}{l}\int{dr/r}\\\\F=\frac{2*9*10^9*3.9*10^{-7}*19*10^{-9}}{0.11}(in(0.02+0.11-in(0.02)))\\\\[/tex]

  • F=2.26*10^{-3}

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