The electric field strength is 276 NC A spherically symmetri

The electric field strength is 276 N/C

A spherically symmetric charge distribution produces the electric field E = ( 4800 r^2)r N/C, where r is in m. What is the electric flux through a 48.0-cm-diameter spherical surface that is concentric with the charge distribution? How much charge is inside this 48.0-cm-diameter spherical surface?

Solution

phi_E = E * phi * d A = E * 4 pi* r²

d = 48 cm, r = d / 2 = 24 cm

= 4800 * 4 pi * (24 * 10^-2)²

= 3474 Nm²/C

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phi_E = q / epsilon₀

q = 3474 * 8.85 * 10^-12

= 3.07 * 10^-8 C