54. Two fixed charges, -4.0 C and -5.0C, areseparated by a certain distance. a.
ID: 1751546 • Letter: 5
Question
54. Two fixed charges, -4.0 C and -5.0C, areseparated by a certain distance. a. Is the net electric field at a location halfway between thetwo charges (1) directed toward the -4.0C charge, (2) zero,or (3) directed toward the -5.0C charge? Why? (b) If thecharges are separated by 20cm, calculate the magnitude of the netelectric field halfway between the charges? a. Is the net electric field at a location halfway between thetwo charges (1) directed toward the -4.0C charge, (2) zero,or (3) directed toward the -5.0C charge? Why? (b) If thecharges are separated by 20cm, calculate the magnitude of the netelectric field halfway between the charges?Explanation / Answer
a. Electric field due to -4.0C = (1/40)* (q1 / r12) *r1^ E1 = 9.0* 109 * ( -4.0 * 10-6) * r1^ /r12 = -(3.6 * 104 / r12) *r1^ N/C Electricfield due to - 5.0C = (1/40)* (q2 / r22) *r2^ E1 = 9.0* 109 * ( -5.0 * 10-6) * r2^ /r22 = -(4.5 * 104 / r22) *r2^ N/C Given r2^ = - r1^ (as point lies at midpoint) and r2 = r1 Netelectric field atmidpoint E = E1+ E2 = - 3.6 *104 *r1^/r2 + (4.5 * 104 / r12) *r1^ E = +(4.5 * 104 / r12) *r1^ field isdirected along r1^ i.e. towardscharge - 4.0 C. b. Putting r1 = 20/2 = 10 cm = 0.1 m E = 4.5* 104 /0.12 = 4.5 *106 N/C Netelectric field atmidpoint E = E1+ E2 = - 3.6 *104 *r1^/r2 + (4.5 * 104 / r12) *r1^ E = +(4.5 * 104 / r12) *r1^ field isdirected along r1^ i.e. towardscharge - 4.0 C. b. Putting r1 = 20/2 = 10 cm = 0.1 m E = 4.5* 104 /0.12 = 4.5 *106 N/CRelated Questions
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