A point charge of magnitude + 1,mu C is fixed | vedclass

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(C) The potential at the center of the sphere is due to the point charge at the origin. Since the sphere is a conductor,the potential is constant thro

Vedclass · Accepted Answer

$2.25 	imes 10^5\,V$ and $-5.625 	imes 10^6\,V/m$

Vedclass · Answer

(C) The potential at the center of the sphere is due to the point charge at the origin. Since the sphere is a conductor,the potential is constant throughout its volume and equal to the potential at its center.$V = \frac{kq}{r} = \frac{9 	imes 10^9 	imes 1 	imes 10^{-6}}{4 	imes 10^{-2}} = 2.25 	imes 10^5\,V$.The electric field inside a conductor is zero. However,the question asks for the induced electric field at the center. The total electric field at the center is the sum of the field due to the point charge $(E_{ext})$ and the field due to the induced charges on the surface of the sphere $(E_{ind})$.Since the net electric field inside a conductor is zero,$E_{net} = E_{ext} + E_{ind} = 0$.$E_{ext} = \frac{kq}{r^2} = \frac{9 	imes 10^9 	imes 1 	imes 10^{-6}}{(4 	imes 10^{-2})^2} = 5.625 	imes 10^6\,V/m$ (directed away from the origin).Therefore,$E_{ind} = -E_{ext} = -5.625 	imes 10^6\,V/m$.

$A$ point charge of magnitude $+ 1\,\mu C$ is fixed at $(0, 0, 0)$. An isolated uncharged spherical conductor is fixed with its center at $(4, 0, 0)$. The potential and the induced electric field at the center of the sphere are:

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