Question

consider a thin plastic rod bent into a semicircular arc of radius R with center at the origin. The rod carries a uniformly distributed negative charge -Q.

(a) Determine the electric field \(\vec{E}\) at the origin contributed by the rod. (Indicate the direction with the sign of your answer. Use any variable or symbol stated above along with the following as necessary: \(\left.\varepsilon_{0} .\right)\)

\(E_{x}=\)

\(E_{y}=\)

(b) An ion with charge \(-4 e\) and mass \(M\) is placed at rest at the origin. After a very short time \(\Delta t\) the ion has moved only a very short distance but has acquired some momentum \(\vec{p}\). Calculate \(\vec{p}\). (Indicate the direction with the sign of your answer. Use any variable or symbol stated above along with the following as necessary: \(\left.\varepsilon_{0} .\right)\)

\(p_{x}=\)

\(p_{y}=\)

Answer 1

(minus sign is token 09 -7P n sa E -dol If ring ble to use into sman fragments, principle of superposition we divide the entire we could be to calculate the ² at o, Ex = -J de cose because the direction da of Ex is opposite of Xai where di = Cinto R² Q total l dl= TER :: Ex= - Sabtu (Ā do) {z coso = Cosa do and dq. Q d 2=Q (R do) Length . rR dq=a do a do A 1 ² r/2 --A zr²ER² 402ER² similarity sino do =0 Ey= dEsito = (site de an?ER² M Ey=0 Could also be arrived using logic of symmetry. - T6/2 72 Q the (b) P = řat = 9,7 st = (-98) (ot î zde at î (Along x-axis) L Р = r² to R²