You have four identical conducting spheres: A, B, C, and D. In each scenario bel

Question

You have four identical conducting spheres: A, B, C, and D. In each scenario below, sphere A starts with a charge of +Q, while B, C, and D start out with no net charge, and then the spheres are touched to each other and separated in the order described. Any spheres not n contact are held very far away. For each scenario, give the final charge of sphere D as a whole number fraction of Q. For example, if you decide that the final charge of sphere D is Q7, enter "1" in the numerator and "7" in the denomi nator Remember! Before each scenario begins, spheres A, B, C, and D are reset to charges of +Q, 0, 0, and 0 again Scenario 1: A and B touch and are separated, then A and C touch and are separated, then A and D touch and are separated o 2: A and B touch and are separated, then B and C touch and are separated, th C and D touch and are separated x Q x Q Scenario 3: A and D touch and are separated, then D and C touch and are separated, then D and A touch and are separated, then A and B touch and are separated x Q

Explanation / Answer

given,

two identical spheres

when identica; uncharged aphere is put in contace with charged sphere charge will flow from high potential to lower potential untill potential difference becomes 0, so if sphere with charge Q will put on contant with uncharged sphere the charge on both the sphere will become Q/2 and Q/2 since the sphere are identical.

scenario 1

when A is touched to B so charge in A left when both are seperated = Q / 2

when A is touched to C so charge in A left when both are seperated = Q / 4

when A is touched to D so charge in A left when both are seperated = Q / 8

same charge will be transferred to sphere D so

QD = Q / 8

scenario 2

when A is touched to B so charge B will gain when both are seperated = Q / 2

when B is touched to C so charge C will gain when both are seperated = Q / 4

when C is touched to D so charge D will gain when both are seperated = Q / 8

so,

QD = Q / 8

scenario 3

when A is touched to D so charge D will gain when both are seperated = Q / 2

when D is touched to C so charge in D left when both are seperated = Q / 4

when again D is touched to A, now A is having charge Q/2 and D is left with charge Q/4

so total charge = Q/2 + Q/4

total charge = 3Q/4

this charge will divide equally between both the spheres so as to make potential difference 0

so charge on D = 3Q/8

QD = 3Q / 8

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