Two plastic spheres The figure shows two thin plastic spherical shells (shown in
ID: 1330190 • Letter: T
Question
Two plastic spheres
The figure shows two thin plastic spherical shells (shown in cross section) that are uniformly charged. The center of the larger sphere is at < 0, 0, 0 >; it has a radius of 12 cm and a uniform positive charge of 5 10-9 C. The center of the smaller sphere is at < 25, 0, 0 > cm; it has a radius of 3 cm and a uniform negative charge of -2 10-9 C.
(a) What is the electric field at location A (6 cm to the right of the center of the large sphere)? Neglect the small contribution of the polarized molecules in the plastic, because the shells are very thin and don't contain much matter. < ,0 , 0>
(b) What is the electric field at location B (15 cm above the center of the small sphere)? Again, neglect the small contribution of the polarized molecules in the plastic, because the shells are very thin and don't contain much matter.
< , , >
(c) What is the force on an electron placed at location B?
< , , >
Explanation / Answer
Field due to a charged spherical sphere at a point inside the shell is zero .
The radius of the sphere is 12 cm and the field at a distance 6cm from the centere (which is inside the sphere) is zero.
b)
The x distance between is 0.25 m
The y distance is given as 0.03 m
The field due to the small sphere at this point is
- 9e9* *2e-9/0.03² = - 2.e4 N/C toward the center of the small sphere.
The component of the field due to the large sphere in this direction at this point is
9e9* 5e-9*/0.03² = 5.e+4 N/C
The net field in this direction is (5-2) e4 = 3 e4 N/C
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The component of the field due to the large sphere in the perpendicular direction at this point is
9e9* 5e-9*/0.25²=7.2 e2
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The net resultant is
{(3 e4)²+ (7.2e2)²} = 3.085 e+4 N/C
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c)
The force on an electron is Ee
3.085 e+4 *1.6e19 = 4.936 e-15 N
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