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Q-2 An infinitely long dielectric cylinder having radius of a and dielectric constant of K=1 are doped with free charges. An infinitely long uncharged dielectric shell which surrounds the cylinder, has inner radius of b=3a and outer radius c=5a and dielectric constant, K=5. Polarization vector at the inner surface of the shell is given by, P(r=b) = 2î and it changes in the shell (>r>b) according to equation: P(r) mộ, where a r Pb(r) is the bounded charge density in the shell. Find an expression for the (a) bounded charge density, (p,o), in terms of a, r (b) electric field vector at r=4a (c) electric field vector at r=a/2 (d) electric field vector at r=6a Note that there is no charge (free+bounded) in the gap between cylinder and shell and no bounded charge in the cylinder.

Q-2 An infinitely long dielectric cylinder having radius of a and dielectric constant of K=1 are doped with free charges. An infinitely long uncharged dielectric shell which surrounds the cylinder, has inner radius of b=3a and outer radius c=5a and dielectric constant, K=5. Polarization vector at the inner surface of the shell is given by, P(r=b) = 2î and it changes in the shell (>r>b) according to equation: P(r) mộ, where a r Pb(r) is the bounded charge density in the shell. Find an expression for the (a) bounded charge density, (p,o), in terms of a, r (b) electric field vector at r=4a (c) electric field vector at r=a/2 (d) electric field vector at r=6a Note that there is no charge (free+bounded) in the gap between cylinder and shell and no bounded charge in the cylinder.

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Q-2 An infinitely long dielectric cylinder having radius of a and dielectric constant of K=1 are doped with free charges. An infinitely long uncharged dielectric shell which surrounds the cylinder, has inner radius of b=3a and outer radius c=5a and dielectric constant, K=5. Polarization vector at the inner surface of the shell is given by, P(r=b) = 2î and it changes in the shell (>r>b) according to equation: P(r) mộ, where a r Pb(r) is the bounded charge density in the shell. Find an expression for the (a) bounded charge density, (p,o), in terms of a, r (b) electric field vector at r=4a (c) electric field vector at r=a/2 (d) electric field vector at r=6a Note that there is no charge (free+bounded) in the gap between cylinder and shell and no bounded charge in the cylinder.
Transcribed Image Text:Q-2 An infinitely long dielectric cylinder having radius of a and dielectric constant of K=1 are doped with free charges. An infinitely long uncharged dielectric shell which surrounds the cylinder, has inner radius of b=3a and outer radius c=5a and dielectric constant, K=5. Polarization vector at the inner surface of the shell is given by, P(r=b) = 2î and it changes in the shell (>r>b) according to equation: P(r) mộ, where a r Pb(r) is the bounded charge density in the shell. Find an expression for the (a) bounded charge density, (p,o), in terms of a, r (b) electric field vector at r=4a (c) electric field vector at r=a/2 (d) electric field vector at r=6a Note that there is no charge (free+bounded) in the gap between cylinder and shell and no bounded charge in the cylinder.
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