A total charge Q is uniformly distributed, with surface charge density

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A total charge Q is uniformly distributed, with surface charge density σ, over a very thin disk of radius R. The electric field at a distance d along the disk axis is given by E→ = σ2ϵ0[1−dd2+R2]n^ where n^ is a normal unit vector perpendicular to the disk. What is the best approximation for the electric field magnitude E at large distances from the disk? a) σ2ϵ0 b) QRϵ0 d2 c) σR4ϵ0 d d) σϵ0(R2 d)2 e) none of the above

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A total charge $Q$ is uniformly distributed, with surface charge density $σ$ , over a very thin disk of radius $R$ . The electric field at a distance $d$ along the disk axis is given by $\vec{E} = \frac{σ}{2 ϵ_{0}} [1 - \frac{d}{\sqrt{d^{2} + R^{2}}}] \hat{n}$ where $\hat{n}$ is a normal unit vector perpendicular to the disk. What is the best approximation for the electric field magnitude $E$ at large distances from the disk? a) $\frac{σ}{2 ϵ_{0}}$ b) $\frac{Q R}{ϵ_{0} d^{2}}$ c) $\frac{σ R}{4 ϵ_{0} d}$ d) $\frac{σ}{ϵ_{0}} {(\frac{R}{2 d})}^{2}$ e) none of the above