Question

Problem 1 (30 points) Two uniformly charged rods with charge Q and length L lie along the z-axis as shown in the figure (rods have been fixed in their positions, so they cannot move). (a)(15pts.) Find the electric field created by the left rod at point I where = > L. (b)(15pts.) Find the electric force on the right rod that is applied by the left rod.

Answer 1

X=0 X=1 X=2L X=31 ca) Electric field direction to left rod for an. y ↑ d X-O X=L Ltd Let us take charge do at a distance ~ foom Origin, Now Electric field due to do at point P. de = kaa C (Ltd) î - x^) (2 : xtd)3 kda (d+L-x)2 da = a de so, E= f d E = Š L(dth-x)? Oo, de a -> KO dn or, E = ka da (d+ L-x)? 1 or, E=kQ L [Cott-x) Ka [ 1 ㅗ dth =ka [ KQ L d (dth) dlater

[6) Force on sight ood F = q ₂ E Now Charge on sod 2 is uniform in oil dibola (0) Take a small charge dq at distance P from origin So force de a de dP (P)(PL) KQ? L2 110 3L or = P2L 9. (0)(P-L) y no mor, & Saf Ska od popo la coll 08, 7 - S del tot of, Fr Ka Set = Kg² [ en 18-27-ene of, F = ka? Sen (21)-en 32 - ence)+ en 24 05, F = km2 [2en( 22) - (en 3L +enz tenu) [ en cas kQ² en (4) Hence this is the required electric force on the right rod along or, F =kQ² L? or ta direction.
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