How Do You Calculate the Electric Field from an Arc?

AI Thread Summary
To calculate the electric field from an arc, the formula E = k*Q/r^2 is used, where k is a constant, Q is charge, and r is distance. The discussion involves integrating to find the electric field, with attempts leading to an expression involving cos(theta) and specific limits. The arc's symmetry about the x-axis allows for integration from -10π/21 to 10π/21, suggesting that the answer should be doubled. The expression theta/sin(theta) is proposed as a potential solution, with theta representing half the angle of the arc in radians. Overall, the integration approach and symmetry considerations are crucial for determining the electric field.
VitaX
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Homework Statement



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Homework Equations



E = k*Q/r^2

The Attempt at a Solution



I tried to get the factor through integrating, but it was wrong.I ended up with (k*lambda*2)/R multiplied by the integral of cos(theta) dtheta. Limits were 10pi/21 and 0. I then divided by k*Q/r^2.
 
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0 to 2π is a complete circle.

The arc appears to be symmetric WRT the x-axis, ∴ integrate cosθ from ‒10π/21 to 10π/21 , which should give twice the answer you had.
 
Is theta/sin(theta) the answer to this problem? theta being in radians and half the angle of the arc.
 
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VitaX said:
Is theta/sin(theta) the answer to this problem? theta being in radians and half the angle of the arc.

I'm sorry, I only looked at your integral in my earlier post. The 2 in the factor preceding your integral makes up for only integrating over half the arc.

Depending upon what you are using for θ, your answer of θ/sinθ looks good.
 

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