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Welcome to this IE. You may navigate to any page youve seen already using the IE tab on the right. Spherical Shell Insulator 0 t P An insulator in the shape of a spherical shell is shown in cross-section above. The insulator is defined by an inner radius a-4 and an outer radius b-6cm and carries a total charge of Q.+9pC(1 μC . 106 C), oou may assume that the charge is distributed uniformly throughout the volume of the insulator). What is Ey, the y-component of the electric field at point P which is located at (x,y)- (0, -5 cm) as shown in the diagram? N/C Submit
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Answer #1

Given is:-

a = 4cm, b=6cm, Q = +9 imes 10^{-6}C

Now,

The volume of the insulator is given by

3 3 3

or

V = rac{4}{3}pi (b^3-a^3)

and the volume of the insulator till the point P is

V_P = rac{4}{3}pi (r^3-a^3)

Volume charge density is

ho = rac{Q}{rac{4}{3}pi (b^3-a^3)}

Now,

the charge enclosed by the region P is

enclosed-P ×

by plugging all the values and simplifying we get

enclosed

Now,

According to the Gauss's law

Qenclosed

or

E = rac{Q (rac{r^3-a^3}{b^3-a^3})}{4 pi r^2 imes epsilon_o}

by plugging all the values we get

(9 x 10-C) T(0.05m)2 x (8.854x 101F/m) (0.06m) 3-(0.04m 7n

which gives us

E= 1.3 × 10 N/C

The charge is uniformly distributed and positive. The field is radially outward. The electric field at (0cm , -5cm) is

E =-1.3 × 10% Ņ/C

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