Two charges are placed on the x axis. One of the charges (q1=. +8.5 μC) is at x1=+3.0 cm and the

step 1 Hi everyone as soon on the figure there are two charges Q1 and Q2 at the position so in figure w

Two charges are placed on the x axis. One of the charges...

Two charges are placed on the $x$ axis. One of the charges $\left(q_{1}=\right.$ $+8.5 \mu \mathrm{C})$ is at $x_{1}=+3.0 \mathrm{cm}$ and the other $\left(q_{2}=-21 \mu \mathrm{C}\right)$ is at $x_{1}=+9.0 \mathrm{cm}$ Find the net electric field (magnitude and direction) at (a) $x=0 \mathrm{cm}$ and (b) $x=+6.0 \mathrm{cm}$

Two charges are placed on the $x$ axis. One of the charges $\left(q_{1}=\right.$ $+8.5 \mu \mathrm{C})$ is at $x_{1}=+3.0 \mathrm{cm}$ and the other $\left(q_{2}=-21 \mu \mathrm{C}\right)$ is at $x_{1}=+9.0 \mathrm{cm}$
Find the net electric field (magnitude and direction) at
(a) $x=0 \mathrm{cm}$ and
(b) $x=+6.0 \mathrm{cm}$

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the force is proportional to the product of the charges and inversely proportional to the square of the distance between them, with a constant of proportionality (k) that depends on the units and the medium. This law is foundational in calculating both forces and the resultant electric fields due to discrete charges.

Electric Field from a Point Charge

The electric field produced by a point charge is defined as the force per unit positive test charge. It is given by the equation E = k|q|/r^2, where 'q' is the point charge, 'r' is the distance from the charge, and 'k' is Coulomb's constant. This concept describes how a charge influences the space around it and is used to compute the field at any given point in space.

Superposition Principle

The superposition principle in electrostatics states that the net electric field created by multiple charges is the vector sum of the electric fields produced by each individual charge. This principle allows for the independent calculation of the fields from each charge, which can then be added together to obtain the overall field at a point.

Direction of Electric Fields

The direction of an electric field due to a charge depends on the sign of the charge. For a positive charge, the field points radially outward, while for a negative charge, it points radially inward. Understanding these directions is crucial for correctly adding vector fields from multiple charges and determining the net field direction.

Distance Dependency in Electric Fields

The magnitude of the electric field from a point charge decreases with the square of the distance from the charge (1/r^2 relationship). This inverse-square law nature means that as one moves further from the charge, the field strength diminishes rapidly, which is an essential consideration when calculating fields at various distances.

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