Two charges of \(5Q\) and \(-2Q\) are situated at the points \((3a, 0)\) and \((-5a, 0)\) respectively. The electric flux through a sphere of radius \(4a\) having its center at the origin is:
Step 1: Analyze the Position of Charges Relative to the Sphere
A sphere of radius \(4a\) centered at the origin includes the charge \(5Q\) located at \((3a, 0)\) since \(3a < 4a\). The charge \(-2Q\) at \((-5a, 0)\) lies outside the sphere since \(5a > 4a\).
Step 2: Apply Gauss’s Law
According to Gauss’s law, the electric flux \(\Phi\) through a closed surface depends only on the net charge enclosed by the surface:
\[
\Phi = \frac{q_{\text{enc}}}{\varepsilon_0}
\]
Since only the \(5Q\) charge is inside the sphere, the enclosed charge \(q_{\text{enc}} = 5Q\).
Step 3: Calculate the Electric Flux
\[
\Phi = \frac{5Q}{\varepsilon_0}
\]
So, the correct answer is: \(\frac{5Q}{\varepsilon_0}\)
Electric flux is a measure of the strength of an electric field passing through a surface. It is defined as the electric field strength times the surface area perpendicular to the electric field. Electric flux is a scalar quantity and is denoted by the symbol ΦE.
The electric flux through a closed surface is equal to the net charge enclosed by that surface, divided by the electric constant. This relationship is known as Gauss's law and is one of the four Maxwell's equations that describe the behavior of electric and magnetic fields.
Electric flux is an important concept in electromagnetism and is used to describe the behavior of electric fields and charges. It is also used to calculate the electric field strength, which is the rate of change of electric flux with respect to distance.
The unit of electric flux is the volt-meter (V m), which is equivalent to the unit of electric field strength. Electric flux has many practical applications, such as in the design and operation of capacitors, electric motors, and generators. It is also used in electrostatic precipitators, which are devices used to remove particulate matter from industrial emissions.
Understanding electric flux is crucial for the development and advancement of modern technology, as it is a fundamental concept in electromagnetism and plays a crucial role in many practical applications.
