Spherical Symmetry (outside sphere): Asphere of radius b has charge distributed uniformly over its volume. We want to find the electric field at a point P a distance from the center of the sphere. Here we assume that ? > b so thatP is outside the sphere. a. From symmetry, which statement below must be true regarding the direction of the electric field? Choose one! i. The electric field points upwards everywhere. i. The E field is tangent to the surface of the sphere everywhere. ii. The E field is radial everywhere. (Radial means away or towards the center of the sphere.) b. From the symmetry, which statement is true regarding the magnitude & = |||| due to the sphere? Choose one! i. E depends on the polar angle only. i. E depends on the distance from the center only. ii. E depends on both and 7. P c. Draw the Gaussian surface you need to determine the electric field at point P. Check that your surface that has ALL the following properties: • The surface must be closed since Gauss's law only holds for closed surfaces. The surface must go through the point P since we want to know the electric field at that point. • The surface must have a = & cose constant on the surface in order to make the flux integral easy.
Spherical Symmetry (outside sphere): Asphere of radius b has charge distributed uniformly over its volume. We want to find the electric field at a point P a distance from the center of the sphere. Here we assume that ? > b so thatP is outside the sphere. a. From symmetry, which statement below must be true regarding the direction of the electric field? Choose one! i. The electric field points upwards everywhere. i. The E field is tangent to the surface of the sphere everywhere. ii. The E field is radial everywhere. (Radial means away or towards the center of the sphere.) b. From the symmetry, which statement is true regarding the magnitude & = |||| due to the sphere? Choose one! i. E depends on the polar angle only. i. E depends on the distance from the center only. ii. E depends on both and 7. P c. Draw the Gaussian surface you need to determine the electric field at point P. Check that your surface that has ALL the following properties: • The surface must be closed since Gauss's law only holds for closed surfaces. The surface must go through the point P since we want to know the electric field at that point. • The surface must have a = & cose constant on the surface in order to make the flux integral easy.
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quesiton 7 and part a,b,c
Transcribed Image Text:Using Gauss's law in situations with high symmetry: The general strategy to find the electric field for situations for high
symmetry is as follows:
♦
Use symmetry to determine the direction of around the object and what variables the magnitude || can
depend on. For example, does E only depend on ?? If there is not enough symmetry, Gauss's law, though still
true, will not be useful for finding the electric field.
Draw a Gaussian (closed) surface such that = E cose must be constant on the surface.
Use the definition of the electric flux = $dA to write the flux in terms of the unknown electric field E.
Determine the charge enclosed by the Gaussian surface and use Gauss's law * = genc/Eo to write a second
expression for the electric flux.
Set the two expressions for the electric flux equal and solve for the unknown E.
2. Spherical Symmetry (outside sphere): Asphere of radius bhas charge distributed uniformly over its volume. We
want to find the electric field at a point P a distance from the center of the sphere. Here we assume that > > b so
that P is outside the sphere.
a. From symmetry, which statement below must be true
regarding the direction of the electric field? Choose one!
The electric field points upwards everywhere.
The E field is tangent to the surface of the sphere
everywhere.
The E field is radial everywhere. (Radial means away or
towards the center of the sphere.)
i.
ii.
iii.
b. From the symmetry, which statement is true regarding the
magnitude E = |||| due to the sphere? Choose one!
i.
E depends on the polar angle only.
ii. E depends on the distance from the center only.
iii. E depends on both and 7.
b
P
C. Draw the Gaussian surface you need to determine the electric field at point P. Check that your surface that has
ALL the following properties:
• The surface must be closed since Gauss's law only holds for closed surfaces.
The surface must go through the point P since we want to know the electric field at that point.
• The surface must have = E co se constant on the surface in order to make the flux integral easy.
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