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Electric Field of Solid Charged Sphere

The electric field of a solid charged sphere describes a vector field that associates to each point in space the Coulomb force that would be experienced per unit of electric charge, by an infinitesimal test charge at that point.

The electric field of a solid charged sphere depends on position, total charge and the radius of the sphere. Outside the sphere, it can be treated as a point charge decreasing with increasing distance. Inside the sphere, the electric potential and field strength drop as one approaches the center.

Formula

{QuantityVariable["ϕ", "ElectricPotential"] == Piecewise[{{(Quantity[Rational[1, 8]/Pi, "ElectricConstant"^(-1)]*QuantityVariable["Q", "ElectricCharge"]*(3 - QuantityVariable["r", "Distance"]^2/QuantityVariable["R", "Radius"]^2))/QuantityVariable["R", "Radius"], QuantityVariable["r", "Distance"] <= QuantityVariable["R", "Radius"]}, {(Quantity[Rational[1, 4]/Pi, "ElectricConstant"^(-1)]*QuantityVariable["Q", "ElectricCharge"])/QuantityVariable["r", "Distance"], QuantityVariable["r", "Distance"] > QuantityVariable["R", "Radius"]}}, 0], QuantityVariable["E", "ElectricFieldStrength"] == Piecewise[{{(Quantity[Rational[1, 4]/Pi, "ElectricConstant"^(-1)]*QuantityVariable["Q", "ElectricCharge"]*QuantityVariable["r", "Distance"])/QuantityVariable["R", "Radius"]^3, QuantityVariable["r", "Distance"] <= QuantityVariable["R", "Radius"]}, {(Quantity[Rational[1, 4]/Pi, "ElectricConstant"^(-1)]*QuantityVariable["Q", "ElectricCharge"])/QuantityVariable["r", "Distance"]^2, QuantityVariable["r", "Distance"] > QuantityVariable["R", "Radius"]}}, 0]}

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Electric Field of Solid Charged Sphere"]
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Get the formula:

In[2]:=
FormulaData[ResourceObject["Electric Field of Solid Charged Sphere"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Electric Field of Solid Charged Sphere"], {QuantityVariable[ "R","Radius"] -> Quantity[1, "Meters"], QuantityVariable["\[Phi]","ElectricPotential"] -> Quantity[10000000000, ("Joules")/("Coulombs")], QuantityVariable["r","Distance"] -> Quantity[1.5`, "Meters"]}]
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