here are many variations of pdaswsx.pptx

here are many variations of p

1. Electric flux Electric flux is a property of an electric field that may be thought of as the number of electric lines of force (or electric field lines) that intersect a given area. Electric field lines are considered to originate on positive electric charges and to terminate on negative charges. Field lines directed into a closed surface are considered negative; those directed out of a closed surface are positive. If there is no net charge within a closed surface, every field line directed into the surface continues through the interior and is directed outward elsewhere on the surface. The negative flux just equals in magnitude the positive flux, so that the net, or total, electric flux is zero. If a net charge is contained inside a closed surface, the total flux through the surface is proportional to the enclosed charge, positive if it is positive, negative if it is negative.

2. Gauss' Law Gauss' law helps us to describe the electric field at a point in space when given an arbitrary distribution of charged particles or surfaces/objects. It is important to note that Gauss' law relies on the application of imaginary surfaces, called Gaussian surfaces, to be used properly. In electrostatics, Gauss' law is most often used to calculate the electric field of a given distribution of charge, but can also be applied to situations where finding electric flux or charge enclosed is desired. By definition, Gauss' law relates the charge enclosed by the Gaussian surface to the field created by that charge. This method is commonly used in problems that have spherical, cylindrical, or cubic symmetries. While symmetry is not a prerequisite for applying Gauss' law, any symmetry present can be used to simplify the mathematics of the problem. Gauss' law tells us that the electric field inside the sphere is zero, and the electric field outside the sphere is the same as the field from a point charge with a net charge of Q.

3. Importance Gauss’s law for the electric field describes the static electric field generated by a distribution of electric charges. It states that the electric flux through any closed surface is proportional to the total electric charge enclosed by this surface. The ultimate goal of Gauss’s law in electrostatics is to find the electric field for a given charge distribution, enclosed by a closed surface. The determination of electric field becomes much simpler if the body due to closed surface exhibits some symmetry in relation to the given charge distribution. Significance of Gauss’ law is that is tells us that electric field origin's from electric charge. Any charge Q� within volume V� enclosed by surface A� , can be thought to give rise to a definite quantity of electric flux through a closed surface A�. If the electric field is known everywhere, Gauss' law makes it possible to find the distribution of electric charge: The charge in any given region can be deduced by integrating the electric field to find the flux.

4. Applying Gauss' Law to a Sphere Gauss' Law states that the total electric flux through a closed surface is equal to the charge enclosed within that surface. This law provides a relationship between the electric field and the distribution of charge that creates that field. When applying Gauss' Law to a sphere, we consider the electric field at any point on the surface of the sphere to be perpendicular to the surface and directed away from the center of the sphere. The electric flux through the sphere can be calculated by taking the dot product of the electric field and the area vector at each point on the surface and then summing over the entire surface. By solving for the electric field, we can determine the distribution of charge within a sphere given the electric field at any point on the surface. This makes Gauss' Law a powerful tool for analyzing and understanding electric field distributions.

5. Outside the sphere E can be pulled out from the integral, where by cancelling like terms, it will become, where is the charged enclosed.     If there are more charges, repeats the calculation for each charges enclosed by the Surface, then add them all. The formula will be   Inside of the sphere Volume Ratio: Electric Flux: 𝛷𝜖 )   Formula: , substitute the constant value of volume ratio.     r  

6. Example Problem 1 An insulating sphere of radius 2m contains +50uc of electric charge uniformly distributed throughout the volume of the sphere. (a) What is the electric field 1.5m away from the center of the sphere? (b) What is the volume charge density. (c) What is the electric field 3.0m away from the center of the sphere?

7. Inside of the sphere      

8. Inside of the sphere      

9. Outside of the sphere    

10. INSIDE THE SPHERE OUTSIDE THE SPHERE EXAMPLE PROBLEM 2

11.   E R=30cm     Inside the Sphere

12.   E=? R=10m   R     Outside the Sphere