A nonconducting disc of radius R and uniform positive surface charge density is placed on the ground with its axis vertical. A particle of specific charge q m = 4 ₀ ~g is dropped along the axis of the disc from a height h . The value of h i

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A nonconducting disc of radius R and uniform positive surface charge density is placed on the ground with its axis vertical. A particle of specific charge q m = 4 ₀ ~g is dropped along the axis of the disc from a height h . The value of h if the particle just reaches the disc is (2 R 3 )^m . Determine the value of m .

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Correct answer: 2

V _ p = 2 ₀ [ R ^2+ h ^2 - h ] ; V ₀= R 2 ₀ To just reach mgh aligned & =q [V₀-V_p ] g h 4 ₀ g = 2 ₀ [R- R^2+h^2 +h ] & h 2 =R+h- R^2+h^2 R^2+h^2 =R+ h 2 & R^2+h^2=R^2+ h^2 4 +R h 3 h^2 4 =R h h= 4 3 R= (2 R 3 )^2 m=2 aligned OR Check dimensionally h= (2 R 3 )^m m=2

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