A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge,of positive charge q.&nbsp;A) What is the total surface charge q on the interior surface of the conductor (i.s., on the wall of the cavity)?&nbsp;C) What is the magnitude&nbsp;E∫&nbsp;of the electric field inside the cavity as a function of the distance from the point charge? Let k, as usual, denote&nbsp;14πϵ0.&nbsp;D)Will the total charge on the surface of the cavity change?&nbsp;Will the totaly charge on the exterior of the conductor change?&nbsp;Will the charge on the electric field with in the cavity change?&nbsp;Will the charge on the electric field outside the cavity change?

Question

A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge,of positive charge q.&amp;nbsp;A) What is the total surface charge q on the interior surface of the conductor (i.s., on the wall of the cavity)?&amp;nbsp;C) What is the magnitude&amp;nbsp;E∫&amp;nbsp;of the electric field inside the cavity as a function of the distance from the point charge? Let k, as usual, denote&amp;nbsp;14πϵ0.&amp;nbsp;D)Will the total charge on the surface of the cavity change?&amp;nbsp;Will the totaly charge on the exterior of the conductor change?&amp;nbsp;Will the charge on the electric field with in the cavity change?&amp;nbsp;Will the charge on the electric field outside the cavity change?

Layton · Accepted Answer

.

Jeffrey Jordon · Accepted Answer

Explanation:  The spherical cavity has a neutral charge. This means that this spherical cavity won´t affect the field inside. Therefore the field generated by the charge q+ is the same with or without the spherical cavity.  The total charge of the system can be calculated considering charge conservation:  Qtot0=Qtotf  q(+)=q(+)+qin+qex  qin=-qex and qin+qex=0  Using a Gaussian sphear centered in the charge q(+), we can calculate the field knowing that its direction would be (r)→  If we apply the gaussian sphear between the interior and the exterior radius of the conducting hollow sphear, knowing that the field should be 0:  ∮sE→ds→=∮s0→ds→=0=qINϵ0=q(+)+qintϵ0  q(+)+qint=0  q(+)=−qint  If we apply the gaussian sphear outside the exterior radius of the conducting hollow sphear, we obtain the field required in c).

A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge,of positive charge q.

Answered question

Answer & Explanation

New Questions in Electromagnetism