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My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.

Here's a question I'm working on that isn't part of my book. question where the radii are a,b,c,da,b,c,d from shortestsmallest to biggestlargest and gray regions are charge distributed insulating spherical shells

Given a,b,c,d,q find E(r) for all the different positions graph it find with charge volume densitiesdistributions.

Given a,b,c,d,q Find:-
1)E(r) for all the different positions
2)Graph E(r)
3)Find volume charge densities

  • I've never done "partial" shaped insulators, my thought process is that since Φ=qiϵ0 and qinqi is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make:

ρ=qV

ρVi=qi

raρ4πr2dr=qi

is this the right process?

  • Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure.

Thanks for any help.

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.

Here's a question I'm working on that isn't part of my book. question where the radii are a,b,c,d from shortest to biggest and gray are charge distributed insulating spherical shells

Given a,b,c,d,q find E(r) for all the different positions graph it find charge volume densities

  • I've never done "partial" shaped insulators, my thought process is that since Φ=qiϵ0 and qin is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make:

ρ=qV

ρVi=qi

raρ4πr2dr=qi

is this the right process?

  • Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure.

Thanks for any help.

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.

Here's a question I'm working on that isn't part of my book. question where the radii are a,b,c,d from smallest to largest and gray regions are insulating spherical shells with charge distributions.

Given a,b,c,d,q Find:-
1)E(r) for all the different positions
2)Graph E(r)
3)Find volume charge densities

  • I've never done "partial" shaped insulators, my thought process is that since Φ=qiϵ0 and qi is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make:

ρ=qV

ρVi=qi

raρ4πr2dr=qi

is this the right process?

  • Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure.

Thanks for any help.

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My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.

Here's a question I'm working on that isn't part of my book. question where the radii are a,b,c,d from shortest to biggest and gray are charge distributed insulating spherical shells

Given a,b,c,d,q find E(r) for all the different positions graph it find charge volume densities

  • I've never done "partial" shaped insulators, my thought process is that since Φ=qinϵ0Φ=qiϵ0 and qin is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make:

ρ=qV

ρVi=qi

raρ4πr2dr=qi

is this the right process?

  • Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure.

Thanks for any help.

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.

question where the radii are a,b,c,d from shortest to biggest and gray are charge distributed insulating spherical shells

Given a,b,c,d,q find E(r) for all the different positions graph it find charge volume densities

  • I've never done "partial" shaped insulators, my thought process is that since Φ=qinϵ0 and qin is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make:

ρ=qV

ρVi=qi

raρ4πr2dr=qi

is this the right process?

  • Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure.

Thanks for any help.

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.

Here's a question I'm working on that isn't part of my book. question where the radii are a,b,c,d from shortest to biggest and gray are charge distributed insulating spherical shells

Given a,b,c,d,q find E(r) for all the different positions graph it find charge volume densities

  • I've never done "partial" shaped insulators, my thought process is that since Φ=qiϵ0 and qin is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make:

ρ=qV

ρVi=qi

raρ4πr2dr=qi

is this the right process?

  • Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure.

Thanks for any help.

Source Link
2c2c
  • 225
  • 3
  • 10

insulator based gauss law questions

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.

question where the radii are a,b,c,d from shortest to biggest and gray are charge distributed insulating spherical shells

Given a,b,c,d,q find E(r) for all the different positions graph it find charge volume densities

  • I've never done "partial" shaped insulators, my thought process is that since Φ=qinϵ0 and qin is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make:

ρ=qV

ρVi=qi

raρ4πr2dr=qi

is this the right process?

  • Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure.

Thanks for any help.