IIT JEE Advanced & Mains Physics 2018 : Electricity : Rank file / expected questions : VII

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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  r\gg a.

 Prove that the electric field varies inversely as the fourth power of r.

56 ] In the above arrangement , E at P is given by – 

A ] E=\frac {3q{a}^{{2}}}{4\pi {\epsilon }_{{0}}{r}^{{4}}}

B ] E=\frac {2q{a}^{{2}}}{3\pi {\epsilon }_{{0}}{r}^{{5}}}

C ] E=\frac {3q{a}^{{3}}}{4\pi {\epsilon }_{{0}}{2r}^{{4}}}

D ] E=\frac {q{a}^{{5}}}{4\pi {\epsilon }_{{0}}{r}^{{4}}}

57 ] On a silk thread attached to a vertical uniformly charged sheet hangs a tiny sphere of mass 3 mg carrying a charge of 9\times {{10}}^{{-8}}{C} .Both gravity and the electric force causes  it to makes an angle of  45^{\circ}with the sheet.Then the charge of the mass is proportional to the surface charge density of the sheet as –

A ] \frac{1}{{q}^{{4}}}

B ] \frac{1}{{q}^{{3}}}

C ] \frac{1}{{q}^{{2}}}

D ] \frac{1}{{q}}

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 \rho , 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  \rho

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  \rho , 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  {r}_{1}, and  outer radius {r}_{2} has it’s middle region filled with a material of resistivity \rho. If  {r}_{{2}}\gg {r}_{{1}} , find the  resistance between the shells

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