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Semicircular charged wire question

  • Thread starter mrtubby
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Homework Statement



Charged Wire laid out in a semicircle, test charge at the center of the "Circle"
what is the charge of dQ. This isn't my whole question but is the bit of it that I cant understand the actual question asks you to go the whole nine yards with calculating the force on the test charge

24eddn7.jpg


The Attempt at a Solution



Charge density: [tex] \frac{total charge}{length of tiny wire piece}=\frac{Q}{\frac{2\pi R}{2}} = \frac{Q}{\pi R} [/tex]

so charge of wire chunk = [itex] \frac{Q}{\pi R} * d\theta [/itex]

when my solution manual uses the charge of the wire chunk it uses [itex] \frac{Q}{\pi R} * d\theta * R [/itex]

I can't figure out why, any hints?
 

Answers and Replies

  • #2
Doc Al
Mentor
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The charge density is charge per unit length. The length of that wire segment is R*dθ, not just dθ.
 

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