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A solid conducting sphere of radius a has net positive charge 2q.a conductinh spherical shell of inner radius b and outer radius c is concentric with solid sphere and has net charge -Q.the surface charge density on inner and outer surface of spherical shell will be?
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A solid conducting sphere of radius a has net positive charge 2q.a con...
Calculation of Surface Charge Density on Inner and Outer Surface of Spherical Shell


Given Data:


  • Radius of solid conducting sphere = a

  • Net positive charge on solid conducting sphere = 2q

  • Inner radius of conducting spherical shell = b

  • Outer radius of conducting spherical shell = c

  • Net charge on conducting spherical shell = -Q



Calculation of Charge on Conducting Spherical Shell:


  • Total charge on solid conducting sphere = 2q

  • As the system is in equilibrium, the net charge on the outer surface of the solid conducting sphere is zero.

  • Therefore, the charge on the inner surface of the conducting shell = 2q

  • As per the principle of charge conservation, the net charge on the conducting spherical shell = -Q

  • Therefore, the charge on the outer surface of the conducting shell = -Q - 2q

  • Hence, the charge on the inner surface of the conducting shell = 2q and the charge on the outer surface of the conducting shell = -Q - 2q



Calculation of Surface Charge Density:


  • The surface charge density on the inner surface of the conducting shell can be calculated as follows:


    • Surface area of the inner surface of the conducting shell = 4πb^2

    • Charge on the inner surface of the conducting shell = 2q

    • Therefore, surface charge density on the inner surface of the conducting shell = (2q) / (4πb^2)


  • The surface charge density on the outer surface of the conducting shell can be calculated as follows:


    • Surface area of the outer surface of the conducting shell = 4πc^2

    • Charge on the outer surface of the conducting shell = -Q - 2q

    • Therefore, surface charge density on the outer surface of the conducting shell = (-Q - 2q) / (4πc^2)




Final Answer:


  • The surface charge density on the inner surface of the conducting shell is (2q) / (4πb^2)

  • The surface charge density on the outer surface of the conducting shell is (-Q - 2q) / (4πc^2)

Community Answer
A solid conducting sphere of radius a has net positive charge 2q.a con...
On inner surface , charge density =. -2q /4πb^2
on outer surface , charge density = -Q / 4πc^2
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