We consider a conducting sphere of radius a = 1m in a uniform electric field E0= 1000 V/m. A uniform field can be thought of as being produced by appropriate positive and negative charges at infinity. Φ = Q/4TTEO (r2R2+2rR cos 0) 1/2 (2² + R2 aQ/4TE0 Q/4 TTED 2rR cos 0)1/2 aQ/4π€0 1/2 1/2 a¹ 2a²r a² 2a²r + COS R2 COS R² R R² R 1 Απευ 20 R² 2Q r cos 0 + 2 a² cos A +... (2.12) (2.13) where the omitted terms vanish in the limit R. In that limit 20/4πTEOR² becomes the applied uniform field, so that the potential is Φ --E (1-5) cos 0 (2.14) 1) Give the derivation process of eq (2.12) 2) Plot the distributions of the potential and current density vector. 3) Compare the results from eq(2.12) and eq(2.14) as R varies.

We consider a conducting sphere of radius a = 1m in a uniform electric field E0= 1000 V/m. A uniform field can be thought of as being produced by appropriate positive and negative charges at infinity. Φ = Q/4TTEO (r2R2+2rR cos 0) 1/2 (2² + R2 aQ/4TE0 Q/4 TTED 2rR cos 0)1/2 aQ/4π€0 1/2 1/2 a¹ 2a²r a² 2a²r + COS R2 COS R² R R² R 1 Απευ 20 R² 2Q r cos 0 + 2 a² cos A +... (2.12) (2.13) where the omitted terms vanish in the limit R. In that limit 20/4πTEOR² becomes the applied uniform field, so that the potential is Φ --E (1-5) cos 0 (2.14) 1) Give the derivation process of eq (2.12) 2) Plot the distributions of the potential and current density vector. 3) Compare the results from eq(2.12) and eq(2.14) as R varies.