Please label the final answer so I know which one to put 17% ooooo T-Mobile LTE
ID: 1528004 • Letter: P
Question
Please label the final answer so I know which one to put
17% ooooo T-Mobile LTE 11:23 AM Wiley PLUS edugen wiley plus.com CES Chapter 23, Problem 050 The figure shows two nonconducting spherical shells fixed in place on an x axis. Shell 1 has uniform surface charge density 3.50 uc/m2 on its outer surface and radius o.200 cm, and shell 2 has uniform surface charge density -2.50 uc/m2 on its outer surface and radius 1.50 cm; the centers are separated by L 7.00 cm. Other than at x oo, where on the x axis is the net electric field equal to zero? Sha Shell 2 units Number the tolerance is +/-2%
Explanation / Answer
The key to solve this problem is first to consider the e-field caused by each nonconducting spherical shell separately, and second superimpose the pictures to find the place where the total electric field equals to zero. Further, since the e-fields caused by both shells are in opposite directions, to find the location to have zero e-field is equivalent to find the location where the magnitudes of both e-fields caused by both shells are the same.
Assume at x cm from the center of shell 1 the total e-field is zero. Use Gauss's law: E•dA = Q/o on the sphere centered at the center of Shell 1 with radius x cm, we have E1 = 3.50*(4*pi*0.2^2)/(4*pi*o*x^2) (with an arbitrary unit).
Now use Gauss's law: E•dA = Q/o on the sphere centered at the center of Shell 2 with radius L-x cm, we have E2 = 2.5*(4*pi*1.5^2)/(4*pi*o*(7-x)^2) (with the same unit as E1).
Since E1 = E2, we have:
3.50*(4*pi*0.2^2)/(4*pi*o*x^2) = 2.5*(4*pi*1.5^2)/(4*pi*o*(7-x)^2)
(3.50*0.2^2)/(x^2) = (2.5*1.5^2)/((7-x)^2)
0.14/x^2 = 5.625/((7-x)^2)
(7-x)^2 = 40.2*x^2
7 - x = 6.34*x
7.34x = 7
x = 0.95