To determine the vector force exerted on charge by charge using Coulomb’s Law, we’ll follow these steps:
Given:
Charge : located at point
Charge : located at point
Coulomb’s Constant :
Coulomb’s Law:
where:
is the displacement vector from to
is the magnitude of
Step 1: Calculate the Displacement Vector
Step 2: Calculate the Distance
Step 3: Apply Coulomb’s Law
Substituting the known values:
Step 4: Calculate the Components
Final Vector Force:
Summary:
The vector force exerted on by is approximately:
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The Deep Dive
To determine the vector force exerted on charge by charge , we first need to calculate the distance between the two charges. The distance can be found using the distance formula:
Plugging in the coordinates, we find . Afterwards, we can apply Coulomb’s law to ascertain the magnitude of the force and the direction by using the unit vector that points from to . The force vector will then combine both magnitude and direction appropriately!
To make it more interesting, think of and as two bickering siblings stuck in a game of tug-of-war: despite their differences, they can’t help but pull each other with a force that depends on how strongly they ‘feel’ about each other! How cool is it to translate their emotions into mathematical expressions?