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A plastic rod having uniformly distributed charge -Q, is bent in a shape of an arc subtending an...

Question:

A plastic rod having uniformly distributed charge -Q, is bent in a shape of an arc subtending an angle of {eq}120^\circ {/eq} at center, point P (origin of the coordinate axis). The axis of symmetry of the rod lies along the x axis and the the radius of the arc is R. In terms of Q and R what is the electric field E due to the rod at point P?

Electric Field:

The electric field is defined as the region around an electric charge in which a test charge experiences an electrostatic force.

It can be expressed as such;

{eq}\vec E = \dfrac{\vec F}{q_{(test)}} {/eq}

Or,

The electric field due to a point charge q at distance r can be expressed as follows;

{eq}\vec E = \dfrac{kq}{r^{2}} \, \hat r {/eq}

Where {eq}k = 9.0 \times 10^{9} \, Nm^{2}C^{-2}. {/eq} and {eq}\hat r {/eq} is a unit vector.

  • The electric fields due to a positive point charge and a negative point charge are directed away from the positive charge and towards the negative charge respectively.
  • The S.I. unit of the electric field is N/C

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We are given that a plastic rod having uniformly distributed charge -Q, and radius of the arc is R. If we consider that the linear charge density be...

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Electric Fields Practice Problems

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Chapter 17 / Lesson 8
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In this lesson, you will be introduced to electric fields so that you can practice calculating single fields, multiple fields, and electric fields in charged spheres. You'll also learn how Faraday cages work.


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