Negative charge is distributed uniformly around three-quarters of a circle of ra

Question

Negative charge is distributed uniformly around three-quarters of a circle of radius a, with the center of curvature at the origin. Use integration to find an algebraic expression for the x and y components of the net electric field at the origin in terms of the linear charge density A and the radius a. Find an algebraic expression for the magnitude and direction of the electric field at the origin. If the distribution has a total charge Q = -25 muC and if a = 5.0 cm, find the numerical value for the electric field's magnitude at the origin.

Explanation / Answer

a) dEx   = K * lambda * ds/a2

=> Integrating from 0 to 3pi/2

=> Ex = K * lambda * (3pi/2)/a                

dEy = K * lambda * ds/a2

=>   Integrating from 0 to pi/2

=> Ey = K * lambda * (pi/2)/a

b)   magnitude of electric field =   K * lambda * (3.162pi/2)/a               

=> direction = tan-1(1/3)

                     =   18.43 degree

c) Electric field =   8.98 * 109 * 106.15 * 10-6 * (3.162 * 3.14/2)/0.05          

                           =   9.464 * 107 N/C

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.