#181 An infinite line of charge with linear density

An infinite line of charge with linear density - Physics

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Free Chegg Question

An infinite line of charge with linear density λ₁ = 7.4 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.3 cm and outer radius b = 4.2 cm. The insulating shell is uniformly charged with a volume density of ρ = -789 μC/m³.

1)

What is λ₂, the linear charge density of the insulating shell?

μC/m

2)

What is E_x(P), the value of the x-component of the electric field at point P, located a distance 8.7 cm along the y-axis from the line of charge?

N/C

3)

What is E_y(P), the value of the y-component of the electric field at point P, located a distance 8.7 cm along the y-axis from the line of charge?

N/C

4)

What is E_x(R), the value of the x-component of the electric field at point R, located a distance 1.15 cm along a line that makes an angle of 30^o with the x-axis?

N/C

5)

What is E_y(R), the value of the y-component of the electric field at point R, located a distance 1.15 cm along a line that makes an angle of 30^o with the x-axis?

N/C

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Free Chegg Answer

1 )

λ₂ =  ( A )

=  (  ( b² - a² )

= - 789 X 3.14 X ( 0.042² - 0.023² )

= - 3.05 μC/m

2)

E_x ( P ) = 0 N/C

because the electric field dos not contian any x - component of field

3 )

E = λ₁ + λ₂ / ( 2  r _o )

E = 7.4 X 10^-6 - 3.05 X 10^-6 / 2 X 3.14 X 0.087 X 8.85 X 10^-12

E = 899636.54 N/C

4 )

E = λ₁ / ( 2  r _o )

E = 7.4 X 10^-6 / 2 X 3.14 X 0.087 X 8.85 X 10^-12

E = 1530416.195 N/C

E_x ( R ) = 1530416.195 X cos30

E_x ( R ) = 1325379.303 N/C

5 )

E_y ( R ) = 1530416.195 X sin30

E_y ( R ) = 662689.65 N/C