Download gauss`s theorem and its applications

GAUSS’S THEOREM AND ITS APPLICATIONS
VERY SHORT & SHORT ANSWER QUESTIONS
1. A ball of charge – 55e lies at the center of a hollow spherical metal shell that has a net charge of – 95e.
What is the charge on (a) the shell’s inner surface and (b) its outer surface ?
2. If Coulomb’s law involved
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r3
dependence
, would Gauss’s law be still true ?
3.
Suppose the enclosing Gaussian surface is changed to (a) a larger Gaussian sphere (b) a Gaussian cube
with edge length equal to r and (c) a Gaussian cube with edge length equal to 2r. In each case, is the net
flux through the new Gaussian surface larger than, smaller than or equal to ?
4. Suppose a Gaussian surface does not include any net charge. Does it necessarily mean that
is equal to
zero for all points on the surface ?
5. A cone of height h and base-radius R is located in a uniform electric field parallel to its base. What amount
of electric flux enters the cone ?
6. Two infinite parallel planes have uniform charge densities ± σ. What is the electric field in : (a) the region
between the planes ? (b) Outside? (c) In what way does the infinite extension of the planes simplify your
derivation ?
7. Is electric flux a scalar or a vector ?
8. A sphere S1 of radius r1 encloses a charge Q. If there is another concentric sphere S2 of the radius r2 (r2>r1)
and there be no additional charges between S1 and S2, find the ratio of electric flux through S1 and S2
9. S1 and S2 are two hollow concentric spheres enclosing charges 2Q and 4Q respectively as shown in Fig.
(1) What is the ratio of electric flux through S1 and S2 ?
(2) How will the electric flux through the sphere S1 change, if a medium of dielectric constant 6 is
introduced in the space inside S1 in place of air ?
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10. State Gauss’s theorem in electrostatics.
11. An electric dipole of dipole moment 20  10-6 C m is enclosed by a closed surface. What is the net flux
coming out of the surface ?
12. A small metal sphere carrying charge +Q is located at the center of a spherical cavity in a large
uncharged metal sphere as shown in Fig . Use Gauss’s theorem to find electric field at points P1 and P2.
LONG ANSWER QUESTIONS
1. Apply Gauss’s theorem to obtain the expression for the electric field intensity at a point due to an
infinitely long, thin, uniformly charged straight wire.
2. State Gauss’s theorem in electrostatics. Use it to obtain an expression for the electric field intensity at a
point near a uniformly charge infinite plane sheet.
3. Using Gauss’s theorem, show mathematically that for any point outside the shell, the field due to a
uniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the
centre. Why do you expect the electric field inside the shell to be zero according to this theorem ?
4. Define electric flux. Write its SI units. A spherical rubber balloon carries a charge that is uniformly
distributed over its surface. As the balloon is blown up and increases in size, how does the total electric
flux coming out of the surface change ? Give reason
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