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Problem 5. Consider a charged sphere with the following charge density 0 r Rmar Using Gauß law, calculate the electric field (a) E inside the sphere (i.e. r 3 Rmar. (b) E2 outside the sphere (i.er2 Rman), (c) Check that-linn E. linn E. Reminder: Due to spherical symmetry JJfv ρ(r)dcdydz dr)Amrndr, max

Consider a charged sphere with the following charge density ρ(r) =(ρ0(1− r Rmax) r ≤ Rmax 0 r > Rmax
Using Gauß’ law, calculate the electric field

(a) ~ E1 inside the sphere (i.e. r ≤ Rmax),

(b) ~ E2 outside the sphere (i.e r ≥ Rmax),

(c) Check that lim r→Rmax ~ E1 = lim r→Rmax ~ E2. Reminder: Due to spherical symmetryRRRV ρ(r0)dxdydz =Rr 0 ρ(r0)4πr02dr0

Please provide an explanation for the solution.

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Answer #1

The net charge enclosed by the sphere at r <Rx is 1S Integrate the above equation. Rax Applying the Gausss law Gauss s law E

7 3 4R E , ForrR, the net electric field is,

馬(4m2)-오 3 4R 쇼뇌 El 128j Now, 7 7 t3 集 @侺): :

3 4R. 12e, And 128/- Hence, (E)=lim,

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