Point charges q1=50 μC and q2=-25 μC are placed 1.0 m apart. What is the force on a third charge

Point charges q1=50 μC and q2=-25 μC are placed 1.0 m apart....

Point charges $q_{1}=50 \mu \mathrm{C}$ and $q_{2}=-25 \mu \mathrm{C}$ are placed $1.0 \mathrm{m}$ apart. What is the force on a third charge $q_{3}=20 \mu \mathrm{C}$ placed midway between $q_{1}$ and $q_{2} ?$

Key Concepts

Superposition Principle

The superposition principle in electrostatics states that the total electric force experienced by a charge is the vector sum of the individual forces exerted by other charges. This principle allows the analysis of complex scenarios by calculating and summing the forces due to each individual charge separately.

Coulomb's Law

Coulomb's Law is a fundamental principle that quantifies the amount of force between two point charges. It states that the electric force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, with the force acting along the line joining the charges.

Electric Force

The electric force is a vector quantity that represents the interaction between electrically charged objects. It has both magnitude and direction, and its value depends on the charge magnitudes, the separation distance, and the sign of the charges involved.

Vector Addition

Since forces are vectors, combining them requires both their magnitudes and directions to be taken into account. Vector addition is crucial when calculating the resultant force acting on a charge, ensuring that the contributions from forces acting in different directions are properly combined.

Transcript

00:01 Okay, and this problem we're told, we have point charges of 15 minus 25 microculems, and they're placed one meter apart.

00:08 So i'll go ahead and draw that q1, q2.

00:17 Fix this a bit.

00:22 Q1 and then q2.

00:25 Some distance are apart.

00:29 You know, r is equal to one meter.

00:35 And then q1 is minus 50.

00:40 Times 10 to the minus 6 coulomes, and q2 is minus 25 times 10 to the minus 6 couloms.

00:56 And we want the force on a third charge, q3, if it's placed midway between these.

01:03 So kind of acknowledging that they're both negative charges, and then acknowledging that q3 is positive, q3 is going to feel an attraction.

01:14 To both so the forces are going to subtract um so the force from q2 i'll call put a little two under here to label that is to the right and so by convention i'll say to the right is positive and then the force from q1 is negative um so adding up the net force we get force is equal to um so we're going to do the force from two so that's k q2 q2 q 3 over r squared and then i'm just going to use magnitudes i'm going to use all positive numbers here i don't have room for the magnitude symbols i'll just put them in okay and then the distance between q3 and q2 is r over 2 so that's going to go in this denominator squared right because the kulom's force is k qqq over r squared and then where r is the actual distance between q3 and q2 which is half of what i'm calling r, which is one meter...

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