Two identical conducting small spheres are placed with their...

Two identical conducting small spheres are placed with their centers 0.300 $\mathrm{m}$ apart. One is given a charge of 12.0 $\mathrm{nC}$ and the other a charge of $-18.0 \mathrm{nC}$ . (a) Find the electric force exerted by one sphere on the other. (b) What If? The spheres are connected by a conducting wire. Find the electric force each exerts on the other after they have come to equilibrium.

Key Concepts

Charge Redistribution on Connected Conductors

When two conductors are connected by a conducting wire, charges redistribute between them until they reach the same electric potential. For identical conductors, this typically results in an equal division of the total charge. This concept helps determine the new charges on each conductor and thus affects the subsequent electric force between them.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges. It states that the magnitude of the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental for calculating the force between isolated charged objects.

Electrostatic Equilibrium in Conductors

In conductors, electrostatic equilibrium occurs when charges have redistributed themselves such that the electric potential is uniform throughout the conductor. In this state, the net electric field inside the conductor is zero, meaning that no further movement of charges occurs. This concept is crucial when understanding how connected conducting objects behave.

Transcript

00:01 Okay, so for question a, we know the electric force is equal to k times q1, times q2 over r squared.

00:07 So q1 is the charge on one sphere, which is one part of charge, 12 nanocolon.

00:13 If we convert the coulone, it's 12 times 10 to 0 .99 cullons, okay? a nanosphere has a charge of negative 18 nanocoulon, which is negative 18 times 102 0 .9 column.

00:23 And r is the distance between the spheres, which is 0 .3 0 meter.

00:28 And therefore, it was asking us the force exerted on each other, so we don't care about the magnitude, which is k, which is 9 .0 times 10 to the power of 9, newtons, times meter square, per klon square.

00:46 Okay? and then times, oh, sorry, 12 times 10 to the power of negative 9 colon, and then times 18 times 10 to the power of negative 9 colon.

01:03 Because we only care about magnitude so we ignore the negative side in this case okay oh sorry and this whole thing over 0 .30 meter and n square and this will give us the electric force exert on each sphere is about 2 .16 times 10 to the power of negative 5 newtown.

01:49 And the direction of this force should be toward each other.

01:52 Okay, because one is positive charge and another one's negative charge.

01:55 That means they were trying to attract each other.

01:57 So let me see.

01:59 Should toward each other.

02:17 Well, question b, so now we connect two severe with a conducting wire.

02:21 So once two severe was connected with the conducting wire, that means the charge will flow from one sphere, one sphere to another severe.

02:31 And it will not stop until the charge on both sides is the same...