Please provide a step by step solution. Thank you so much for your assistance! :

Question

Please provide a step by step solution. Thank you so much for your assistance! :)

Three nonconducting strips are bent to form arcs and, when assembled, they form part of a circle of radius r-6.45 cm. The three strips have linear charge densities of -88.0 nC/m, =-179 nC/m, and 3 = 268 nC/m, respectively, and subtend angles of 60°, 120°, and 45°, respectively, at the center. 120 450 23 (a) Determine the electric potential at the center of the circle of which the strips form a part. (b) You use a fourth nonconducting strip to close the circle. What should be the linear charge density on this strip if the potential at the center of the circle is to be zero? nC/m

Explanation / Answer

V = k Q / R

R = 6.45 cm = 0.0645 m

Q1 = lambda1 (r theta1 )

Q1 = (88 nC/m)(2 pi x 0.0645 x 60 / 360) = 5.944 nC  

Q2 = (-179)(2pi x 0.0645 x 120 / 360) = - 11.89 nC  

Q3 = (268) (2pi x 0.0645 x 45 / 360) = 4.458 nC

(A) V = (k / R) (Q1 + Q2 + Q3)

  
V = (9 x 10^9) (5.944 - 11.89 + 4.458)(10^-9) / 0.0645

V = - 207.6 Volt .....Ans

(B) for forth part Q4,

Q1 + Q2 + Q3 + Q4 = 0

q4 = 1.488 nC  

length of forth piece = (0.0645)(2 pi (360 - 60 - 120 - 45)/360)

L = 0.152 m

lambd2 = Q4 / L

= 9.79 nC/m

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