A point charge of -2.10 �C is located in the center of a spherical cavity of radius 6.54 cm inside an insulating spherical charged solid. Th

Question

A point charge of -2.10 �C is located in the center of a spherical cavity of radius 6.54 cm inside an insulating spherical charged solid. The charge density in the solid is 7.36 x 10-4 C/m3. Calculate the electric field inside the solid at a distance of 9.48 cm from the center of the cavity. (magnitude and direction)

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Kiệt Gia 4 years 2021-08-17T19:44:38+00:00 1 Answers 20 views 0

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  1. Euphemia
    0
    2021-08-17T19:46:07+00:00
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    Answer:

    -3.4\times 10^5 N/C

    Explanation:

    We are given that

    q_0=-2.1\mu C=-2.1\times 10^{-6} C

    1\mu C=10^{-6} C

    r_1=6.5 cm=6.54\times 10^{-2} m

    1 m=100 cm

    r_2=9.48 cm=9.48\times 10^{-2} m

    \rho=7.36\times 10^{-4} C/m^3

    We have to find the electric field inside the solid at distance of 9.48 cm from the center of the cavity.

    Volumetric charge density,\rho=\frac{Q}{V}

    Charge on spherical solid=Q=V\rho=\frac{4}{3}\pi(r^3_2-r^3_1)\rho

    Q=\frac{4}{3}\pi((9.48\times 10^{-2})^3-(6.54\times 10^{-2})^3)\times 7.36\times 10^{-4}=1.76\times 10^{-6} C

    Electric field =Electric field due to spherical charge solid +electric field due to charge at center

    E=\frac{KQ}{r^2}+\frac{Kq_0}{r^2}=\frac{k}{r^2}(Q+q_0)

    Where k=9\times 10^9

    E=\frac{9\times 10^9\times}{(9.48\times 10^{-2})^2}(1.76\times 10^{-6}-2.1\times 10^{-6})=-3.4\times 10^5 N/C

    Where  negative sign indicates that the direction of electric field is inward.

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