What is the Electric Field Equation for an Electrified Sphere?

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In summary, the electrified sphere problem is a theoretical physics problem used to determine the electric potential and electric field around a charged spherical object. The electric potential can be calculated using the equation V = kQ/r, while the electric field is a measure of the force per unit charge at a given point. As the distance from the sphere increases, both the electric potential and electric field decrease. This problem has real-world applications, such as understanding the behavior of charges in electric circuits and predicting the behavior of particles in particle accelerators.
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omar558
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Homework Statement
The function that expresses the electric potential of a metallic electrified sphere is kQ/R if 0<r<R and kQ/r if r>R k=9 × 10^9 Nm2/c2
Find, starting from the electric potential function, the electric field function
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Conceptual
I don't know if i can use V=E · d. I've read about gradient but i never used it so i was asking if there is another way to get tje electric field equation
 
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  • #2
Look up the expression for gradient in spherical coordinates and set to work. It is not complicated.
 
  • #3
Or you could express V = V(Q,r) then us Gauss's theorem. For r<R remember where the charge lies on a metallic mass.
 

Related to What is the Electric Field Equation for an Electrified Sphere?

1. What is the electrified sphere problem?

The electrified sphere problem is a theoretical physics problem that involves calculating the electric field and potential around a charged sphere. It is commonly used to demonstrate the principles of electrostatics and is a fundamental concept in electromagnetism.

2. How is the electric field calculated for an electrified sphere?

The electric field around an electrified sphere can be calculated using the formula E = kQ/r^2, where E is the electric field, k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere. This formula is valid for points outside the sphere.

3. What is the potential around an electrified sphere?

The potential around an electrified sphere can be calculated using the formula V = kQ/r, where V is the potential, k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere. This formula is valid for points outside the sphere and is measured in volts.

4. How does the electric field and potential change as you move closer or further away from the electrified sphere?

The electric field and potential both decrease as you move further away from the electrified sphere. This is because the electric field and potential are inversely proportional to the distance from the center of the sphere. As you move closer to the sphere, the electric field and potential increase.

5. Can the electrified sphere problem be applied to real-life situations?

Yes, the concepts and calculations involved in the electrified sphere problem are used in various real-life situations, such as designing electrical circuits, understanding lightning strikes, and studying the behavior of charged particles in space. It is a fundamental concept in electromagnetism and has numerous practical applications.

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