Consider a thin plastic rod bent into an arc of radius R and angle a (see figure below). The rod carries a uniformly distributed negative charge -Q. R What are the components E, and E, of the electric field at the origin? Follow the standard four steps. (a) Use a diagram to explain how you will cut up the charged rod, and draw the AF contributed by a representative piece. a (b) Express algebraically the contribution each piece makes to the and y components of the electric field. Be sure to show your integration variable and its origin on your drawing. (Use the following as necessary: Q, R, a, 0, A0, and Eg-) ΔΕ, ΔΕ, - 4ne aR² E₂ Ey @__a sin 6 X 4ne, aR (c) Write the summation as an integral, and simplify the integral as much as possible. State explicitly the range of your integration variable. Lower limit= 0 ✓ de cose X Upper limit= a ✓ Evaluate the integral. (Use the following as necessary: Q, R, a, and EQ.) -sin(a) 4nz aR² Ane aR² (1 cosa) Edit

Consider a thin plastic rod bent into an arc of radius R and angle a (see figure below). The rod carries a uniformly distributed negative charge -Q. R What are the components E, and E, of the electric field at the origin? Follow the standard four steps. (a) Use a diagram to explain how you will cut up the charged rod, and draw the AF contributed by a representative piece. a (b) Express algebraically the contribution each piece makes to the and y components of the electric field. Be sure to show your integration variable and its origin on your drawing. (Use the following as necessary: Q, R, a, 0, A0, and Eg-) ΔΕ, ΔΕ, - 4ne aR² E₂ Ey @__a sin 6 X 4ne, aR (c) Write the summation as an integral, and simplify the integral as much as possible. State explicitly the range of your integration variable. Lower limit= 0 ✓ de cose X Upper limit= a ✓ Evaluate the integral. (Use the following as necessary: Q, R, a, and EQ.) -sin(a) 4nz aR² Ane aR² (1 cosa) Edit