State gauss's theorem draw a graph showing the variation of electric field, as one moves from the centre of charge metal ball to a point on its surface and then to a far off outside point
Gauss's Law. The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field.
E=kq/r^2, so the graph should show a 1/r^2 graph.
Ah, Gauss's theorem, the beloved mathematician Carl Friedrich Gauss wouldn't be too pleased with my attempt at humor on this serious topic, but here we go!
Gauss's theorem states that the electric flux passing through a closed surface is equal to the net charge enclosed by the surface divided by the permittivity of the medium. Fancy stuff, right?
Now, let's visualize this journey from the center of a charged metal ball to a point on its surface, and then to a far off outside point. Unfortunately, I'm just a text-based bot, so I can't draw you a fancy graph. But imagine this:
As you move from the center towards the surface of the metal ball, the electric field strength would gradually decrease. Think of it as being in the middle of a crowd of excited clowns and moving closer to the edge — the chaos subsides a bit.
Once you reach the surface of the ball, the electric field would be perpendicular to the surface and pointing outward. Maybe like the clowns, they're pushing you away politely but firmly, maintaining personal space.
As you venture even further away from the ball, towards an outside point, the electric field strength would continue to decrease, becoming weaker and weaker. Imagine the clowns waving goodbye but their enthusiasm dwindling as you leave their circus tent.
Remember, this is just a simplified visualization. The graph would typically show a decrease in electric field strength as you move away from the center of the charged metal ball. But hey, at least you got to imagine clowns along the way!
Gauss's theorem, also known as Gauss's law, relates the electric flux through a closed surface to the charge enclosed by that surface. It can be stated as follows:
The net electric flux through any closed surface is proportional to the total charge enclosed by that surface divided by the electric constant (also known as the permittivity of free space, denoted by ε₀).
Mathematically, Gauss's theorem can be expressed as:
∮E · dA = Q_enclosed / ε₀
where:
- ∮E · dA represents the surface integral of the electric field E dotted with the infinitesimal vector dA.
- Q_enclosed stands for the total charge enclosed by the closed surface.
- ε₀ represents the electric constant or permittivity of free space, approximately equal to 8.85 × 10⁻¹² C²/(N·m²).
Now, let's consider a scenario where we have a metal ball with a positive charge at its center. We want to analyze the variation of the electric field as we move from the center of the ball to a point on its surface, and then to a far-off outside point.
To begin with, at the center of the ball, the electric field due to the positive charge will be directed radially outwards and will have the maximum magnitude. As we move towards the surface of the ball, the electric field will get weaker due to the increasing distance from the charge.
Upon reaching the surface of the ball, the electric field at that point will be tangential to the surface and directed entirely away from it. This is because, in a conductor, the electric field inside is zero due to the redistribution of charges that occurs to achieve electrostatic equilibrium.
For points beyond the surface of the ball (far-off outside points), the electric field will follow the inverse square law. It will decrease rapidly as the distance from the center of the ball increases. The exact value and direction of the electric field at these far-off points will depend on the magnitude and distribution of charges in the surrounding environment.
Unfortunately, as an AI text-based assistant, I'm unable to draw a graph directly. However, I can describe the general trend of the electric field graph. As you move from the center of the ball to a point on its surface, the magnitude of the electric field decreases. Then, at the surface, it becomes zero due to the properties of conductors. Lastly, as you move to a far-off outside point, the magnitude of the electric field decreases rapidly following the inverse square law.
Gauss's theorem, also known as Gauss's law, relates the electric flux through a closed surface to the charge enclosed by that surface. Mathematically, Gauss's theorem can be stated as:
∮ E · dA = (1/ε₀) ∫ ρ dV
Where:
- ∮ E · dA is the flux of the electric field E through a closed surface,
- ρ is the charge density (charge per unit volume),
- ε₀ is the permittivity of free space, and
- ∫ ρ dV is the integral of the charge density over the volume enclosed by the surface.
Now, let's consider a scenario where there is a charged metal ball. When we move from the center of the ball to a point on its surface and then to a far-off point outside the ball, there are a few key things to keep in mind:
1. Center of the ball: At the center of the charged metal ball, the electric field is zero. This is because the electric field created by each charged particle on the ball is canceled out by the opposite charges in the ball.
2. Point on the surface: As we move from the center to a point on the surface of the ball, the electric field gradually increases. It points radially outward from the center and its magnitude decreases with increasing distance from the center. The electric field at any point on the surface is directly proportional to the charge enclosed by that point divided by the surface area.
3. Far-off outside point: As we move further away from the surface of the ball to a far-off outside point, the electric field decreases rapidly. The electric field at points outside the charged ball follows the inverse square law, which means it decreases with the square of the distance from the center of the ball.
Now, let's consider the graph showing the variation of electric field as we move from the center of the charged metal ball to a point on its surface and then to a far-off outside point:
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E | | |
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\|/ <|> <|> <|>
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Surface Far-off outside
of the ball point
In the graph, the horizontal axis represents distance from the center of the charged metal ball, and the vertical axis represents the magnitude of the electric field. The electric field gradually increases as we move from the center towards the surface of the ball. On the surface, it reaches its maximum value (which depends on the charge enclosed by that point and the surface area). As we move to a far-off outside point, the electric field decreases rapidly following the inverse square law.
It's important to note that the exact shape of the graph will depend on the charge distribution and the geometry of the metal ball.