## Question

###### 2. Positive charge Q is distributed uniformly on the left quarter and negative charge -Q is...

2. Positive charge Q is distributed uniformly on the left quarter and negative charge -Q is distributed on the right quarter of the semicircle of radius a, in Figure on the right. (i) Calculate x and y component of the electric field at the center of the semicircle. (20 points) Find the Coulomb force acting on a negative charge placed at the center of the semicircle. (5 1 points)

## Answers

0 o Due to fy The eletrie field at due to -Q is y E which have two componento Ex and efefrie field value at o Sime butį direction is different. How due to Symmetry then the Component Cancel only the due to tQ ; Ey Eg Ex remain For Section of element as the eletrie field at a 0 TAS Sino [I donsili y line charge 4 Ex av density 476 hezz 4S a do 4Ex- * Į sino do Yato Semi cirele Ex=ytta Coso so 1 4+ta EX Ytta 216, .. now ta E a anato a negative charge. I is a F ih Force on Ex 9. Q9 21ăto

12 IT I 19 20 21 22 124 125 28 30 -9 20 Ta GV + 0 TIRA t We can see that the vertical Component gels Concelled out quarters ESMO 11 for both * * o 12 o E logo EGe 01 F Only horizontal Component adds up 02 om Esind 9 abodo xx Change do stup 03 Coso I 4560 04 05 Glo for left Quarter 06 4flito Taxa [ Simo] 2Q 2 a 4926a? [sione non Sing 492&a? 22 10 49² & 2² 26 Notes 47? & a?FEBRUARY 요 FR 1 x 29 caso do R 4760 na 0 aso do za 4926. a? احد Right le Sino] 40? & ? ? Some side 20 477? & a? 2Q 40°C a 04 B 17 os i. Total Field & & & ER 06 2x 20 4026a? 40 P-40?6, a? acting towards +ve a axis Notes Coulomb face negative 40

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