A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center. = The radial component of the electric field at a point that is 0.60 m from the center is closest to
A) zero.
B) +5000 N/C.
C) +7500 N/C.
D) -5000 N/C.
E) -7500 N/C.

Question

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center.  =  The radial component of the electric field at a point that is 0.60 m from the center is closest to 
A) zero. 
B) +5000 N/C. 
C) +7500 N/C. 
D) -5000 N/C. 
E) -7500 N/C.

Quizplus · Accepted Answer

Since the point charge is at the center of the sphere, it will not affect the radial component of the electric field at a point that is at a distance of 0.60 m from the center. Therefore, we only need to consider the electric field due to the net excess charge on the spherical shell.

The electric field due to a uniformly charged spherical shell with a net charge Q and radius R at a point outside the shell is given by:

E = k(Q/R^2)

where k is the Coulomb constant.

At a distance of 0.60 m from the center of the sphere, the radial distance from the center of the spherical shell is 0.60 - 0.80 = 0.20 m. Therefore, the electric field at this point is:

E = k(Q/R^2) = (9 x 10^9 N*m^2/C^2)(-500 x 10^-9 C)/(0.8 m)^2 = -7500 N/C

The negative sign indicates that the electric field points inward, towards the center of the spherical shell. Therefore, the best choice is C: -7500 N/C.

A Hollow Conducting Spherical Shell Has Radii of 0