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An electric dipole of dipole moment oversetto pconsists of point charges +q and -q separated by a distance '2a' apart. Deduce the expression for the electric field oversetto Edue to the dipole on its axial line in term of the dipole moment oversetto p. Hence show that in the limitr gt gt a, oversetto E =(2 oversetto p)/( 4 pi in _0 r^(3)) (b) Given the electric field in the region oversetto E = 2x hatiFind the net electric flux through the cube and the charge enclosed by it. |
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Answer» Solution :As ELECTRIC field is given by ` overset to E = 2x hati ` , it is OBVIOUS that electric flux `phi_in = int oversetto E . overset to (ds) ` is finite for onlytwo surface marked 1 and 2 in which lie in Y-Zplane and for all remaining four surface of cube flux is zero . Here AREA of each surface `s= a^(2) ` For face 1,x =0 and `oversetto E = 0 ` . Therefore electric flux ` phi_1 =0.` For face 2,x = a and `oversetto E =2 a hati` , Therefore electric flux ` phi _2 = overset to E . oversetto s= (2 a hati).( a^(2)hatl )= 2a^(3) ` ` therefore ` Net electric flux through the cube`phi_in =phi_1+phi_2 =0 =2a^(3) =2a^(3) ` and the charge enclosed by the cube `q= in_0 phi_in =in_0 2a^(3) =2 in_0 a^(3) ` ` (##U_LIK_SP_PHY_XII_C01_E11_002_S01.png" width="80%"> |
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