Quiz9-2007-102

# Quiz9-2007-102 - NAME: STUDENT NO: SIGNATURE: DEPARTMENT...

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Unformatted text preview: NAME: STUDENT NO: SIGNATURE: DEPARTMENT PHYSICS 102- Summer School- Instructor: M. Özgür OKTEL- June 26, 2006 QUIZ-9 A non-conducting thin annulus of inner radius a and outer radius b is placed on the x-y plane. If the annulus is uniformly charged with total charge Q, a) Find the surface charge distribution σ on the annulus. b) Find the potential V at a point z above the axis of the annulus. z b a SOLUTIONS a) σ= Q A For an annulus inner radius a and outer radius b; A = π (b 2 − a 2 ) Q σ= 2 π (b − a 2 ) b) To find the potential at a point z, we consider concentric rings with infinitesimally small width dr. z D=(r2 + z2)1/2 b a r dr dq 4πε o D dq = σ 2π rdr σ 1 σ 2π rdr dV = = 4πε o z 2 + r 2 2ε o dV = 1 rdr z2 +r2 σ σ b = ( z 2 + r 2 )a = ( z 2 + b2 − z 2 + a2 ) 2ε o 2ε o σ V = ∫ dV = 2ε o Put σ = b ∫ a rdr z2 +r2 Q 2 π (b − a 2 ) Q V= ( z 2 + b2 − z 2 + a2 ) 2 2 2πε o (b − a ) ...
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Quiz9-2007-102 - NAME: STUDENT NO: SIGNATURE: DEPARTMENT...

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