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Problem 3 Problem: A point charge with charge +Q is surrounded by a charged conducting shell, with total charge -2Q, of inner radius a and outer radius b. Outside of the shell is an uncharged dielectric shell of inner radius b and outer radius c, with dielectric constant K = 3. -20 IV III II (a)What is the field in region 1? (b)What is the field in region I1? (c)What is the field in region III? (d)What is the field in region IV? (e)What is the charge on inner surface of the conductor Qe,inner? Air Conductor (f)What is the charge on the outer surface of the con- ductor Qe,outer? Dielectric (g)What is the bound charge on the inner surface of the dielectric Qd,inner?

Problem 3 Problem: A point charge with charge +Q is surrounded by a charged conducting shell, with total charge -2Q, of inner radius a and outer radius b. Outside of the shell is an uncharged dielectric shell of inner radius b and outer radius c, with dielectric constant K = 3. -20 IV III II (a)What is the field in region 1? (b)What is the field in region I1? (c)What is the field in region III? (d)What is the field in region IV? (e)What is the charge on inner surface of the conductor Qe,inner? Air Conductor (f)What is the charge on the outer surface of the con- ductor Qe,outer? Dielectric (g)What is the bound charge on the inner surface of the dielectric Qd,inner?

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Problem 3 Problem: A point charge with charge +Q is surrounded by a charged conducting shell, with total charge -2Q, of inner radius a and outer radius b. Outside of the shell is an uncharged dielectric shell of inner radius b and outer radius c, with dielectric constant x = 3. -2Q IV III I (a)What is the field in region 1? (b)What is the field in region II? (c)What is the field in region III? I (d)What is the field in region IV? Air (e)What is the charge on inner surface of the conductor Qe,inner? (f)What is the charge on the outer surface of the con- ductor Qe,outer? Conductor Dielectric (g)What is the bound charge on the inner surface of the dielectric Qa,inner? (h)What is the bound charge on the outer surface of the dielectric Qd,outer?
Transcribed Image Text:Problem 3 Problem: A point charge with charge +Q is surrounded by a charged conducting shell, with total charge -2Q, of inner radius a and outer radius b. Outside of the shell is an uncharged dielectric shell of inner radius b and outer radius c, with dielectric constant x = 3. -2Q IV III I (a)What is the field in region 1? (b)What is the field in region II? (c)What is the field in region III? I (d)What is the field in region IV? Air (e)What is the charge on inner surface of the conductor Qe,inner? (f)What is the charge on the outer surface of the con- ductor Qe,outer? Conductor Dielectric (g)What is the bound charge on the inner surface of the dielectric Qa,inner? (h)What is the bound charge on the outer surface of the dielectric Qd,outer?
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a) charge in region I is +Qso, field in region I is,E→.ds→ =Qε0E×4πr2=Qε0E=Q4πε0r2r <ab) E→.ds→ =Qε0E×4πr2=Qε0E=Q4πε0r2a<r<bc)charge in region III)E→.ds→ =QεE×4πr2=(Q-2Q)ε0εr  (εr=3)E=14πε0r2-Q3r2b<r<c

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