What is the Electric Field Equation for an Electrified Sphere?

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The electric field equation for an electrified sphere can be derived using the gradient in spherical coordinates. It is suggested to express the potential V as a function of charge Q and radius r, then apply Gauss's theorem for calculations. For points inside the sphere (r<R), it's important to consider the distribution of charge on a metallic surface. The discussion emphasizes that while using V=E·d may seem unclear, alternative methods exist that simplify the process. Understanding these concepts is crucial for accurately determining the electric field around an electrified sphere.
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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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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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Look up the expression for gradient in spherical coordinates and set to work. It is not complicated.
 
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.
 

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