The electric field at arbitrary point outside the sphere is determined as the E = σr³/k.
Electric field determined from Gauss law
The electric field of the surface is determined from Gauss law as shown below;
E ∫ds = Q/ε
E (4πr²) = Q/ε
E = Q/4πεr² . r
[tex]E = \frac{Q R}{4\pi \varepsilon r^3}[/tex]
Electric field outside the sphere with dielectric with polarization
[tex]P = \frac{\sigma}{E} \\\\E = \frac{\sigma}{P}[/tex]
[tex]E = \frac{\sigma}{k/r^3} \\\\E = \frac{\sigma r^3}{k}[/tex]
where;
- σ is dipole moment of atom of the metal
- k is dielectric constant
Thus, the electric field at arbitrary point outside the sphere is determined as the E = σr³/k.
The complete question:
A metal sphere of radius R carries a total charge Q. outside the sphere is a dielectric with polarization p(f) k/r^3er. Determine the electric field at arbitrary point outside the sphere.
Learn more about electric field here: https://brainly.com/question/14372859
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