A thin rod bent into the shape of an arc of a circle of radius R carries a unifo

Question

A thin rod bent into the shape of an arc of a circle of radius R carries a uniform charge per unit length lambda = 2.30E-9 C/m. The arc subtends a total angle 2 theta 0, symmetric about the x axis, as shown in the figure below. Theta 0 = 21.00 and R = 0.22 m. Determine the magnitude of the electric field E at the origin 0. (For reference see class notes) hard to avoid integrating for this one but at least the integral isn?t too bad. Remember that the problem asks for the magnitude of the electric field.

Explanation / Answer

Here ,

half angle , theta = 21 degree

charge density , Lamda = 2.3 *10^-9 C/m

for a circular arc the eletic field is given as

electric field , E = k*lamda*(2 * sin(theta))/r

E = 9*10^9 * 2.3 *10^-9 *( 2 * sin(21))/0.22

solving for E

E = 67.43 N/C

the electric field at the centre of arc is 67.43 N/C

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