Question

# Q1 A hollow spherical conductor of internal radius R₂ and external radius R3 surrounds a conductive sphere of radius R₁, which is charged with a charge Q,as shown in Figure Q1.

Derive the expression for the magnitude of the electric field E(r), for between 0 and ∞o. Note that r = 0 is the origin of the spherical reference system, as shown in Figure Q1.[16] Hence or otherwise, derive the expression for the scalar potential V(r),for r between 0 and ∞. ing R₁Give a qualitative graphical representation for the functions E(r)(magnitude of the electric field) and V(r) (scalar potential), consider-160 cm, and Q = 80 × 10-¹2 C.Use the appropriate units on the graphs. Write the values of the electric field in the dielectric side of the interface for each of the metallic 60 cm, R₂ =100 cm, R3:=surfaces. Write the values for the potential at r = 0, r = R₁, r = R₂, [12]and r = R3.= Briefly describe what happens to the scalar potential and electric field in the region with R₁ < r < R₂ at the static equilibrium if a charged sphere of radius Rs = 50 cm and charge Qs = 2 × 10-6 C is positioned close to the hollow conductor, with its centre at R₁ == 4 m. Include a [10]brief explanation for your answer.

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