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55 – 56 ] Consider four charges q, q,−q,−q that are located at the corners of a square of side a . At a distance r from the center of this arrangement , a point P is chosen in the same plane. Here .
Prove that the electric ﬁeld varies inversely as the fourth power of r.
56 ] In the above arrangement , E at P is given by –
57 ] On a silk thread attached to a vertical uniformly charged sheet hangs a tiny sphere of mass 3 mg carrying a charge of .Both gravity and the electric force causes it to makes an angle of with the sheet.Then the charge of the mass is proportional to the surface charge density of the sheet as –
58 ] In the above case , calculate the surface charge density .
59 – 62 ] Consider an infinite slab of thickness 2d whose other two dimensions are inﬁnite.If it’s volume charge density is , find the electric ﬁeld at a point on it’s surface .
60 ] If 1/3 rd of the value of the electric field of the above case is calculated , it’s the same as that of a ————- of the same volume charge density
A ] cylinder
B ] sphere
C ] cone
D ] hemisphere
61 ] In fact comparing the electric field of the slab ( sl ) of question 60 with that of a cylinder ( cy ) and sphere ( sp) , of the same volume charge density , the field strength in descending order is –
A ] cy > sp > sl
B } sp > cy > sl
C ] cy > sl > sp
D ] sl > cy > sp
62 ] Discuss the key theoretical point which causes the difference in field strengths regarding the above case . .
63 ] Two concentric spherical shells of inner radius , and outer radius has it’s middle region ﬁlled with a material of resistivity . If , find the resistance between the shells