Question

Question 1 (compulsory): The following set of charges is given in free space Charge σ,--40 nC/m Number and type of charge #1 , charged spherical shell of radius Ri-10 cm carrying uniform surface charge density σ #2, charged spherical shell of radius R2-5 cm carrying uniform surface charge density Ơ Location (0, 0, 0) m (position of the centre of the sphere) (0, 0, 0) m (position of the centre of the sphere σ,-160 nC/m2 The positions of the spheres' centres coincide which means that they are concentric, similarly to the concentric spherical capacitor. #3, point charge q37 nC #4, point charge (i) Sketch schematically and explain the net electric field (E-field) due to spheres #1 and #2 (neglecting the presence of charges #3 and #4) 20% (ii) Find the voltage between the points a-(2, 2,-2) m and b-2, 3, 0) m due to point charges #3 and #4 (neglecting the presence of spheres #1 and #2) 25% (iii) Find the total electric flux due to all charges of this question passing through "Gaussian" spheres of radius Ri-7 cm, R2-20 cm and Rs-3 m, all centred on the origin. 20% (iv) Gauss' law for the electric field states that the closed surface integral of the flux density D over any closed surface is equal to the charge enclosed by that surface. Using an infinite line of charge as an example of a system that possesses (cylindrical) symmetry, show that Gauss' law can be reduced to the expression D- A- configuration 35% qand hence can be used to find the electric field due to his encl

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