An electric dipole is formed by two charges + q and - q located in x y -plane at ( 0 ,   2 )   mm and ( 0 ,   − 2 )   mm , respectively, as shown in the figure. The electric potential at point P ( 100 ,   100 )   mm due to the dipole is V 0 . The charg

Question

An electric dipole is formed by two charges  + q and - q located in x y -plane at ( 0 , &#160; 2 ) &#160; mm and ( 0 , &#160; &#8722; 2 ) &#160; mm , respectively, as shown in the figure. The electric potential at point P ( 100 , &#160; 100 ) &#160; mm due to the dipole is  V 0 . The charges + q and &#8211; q are then moved to the points ( &#8722; 1 , &#160; 2 ) &#160; mm and ( 1 , &#160; &#8722; 2 ) &#160; mm , respectively. What is the value of electric potential at P  due to the new dipole?

Quantrex Academy · Accepted Answer

Correct answer: B. V 0 2

Electric potential at any general point for vertical dipole is written as,  V 1 &#8733; p 1 cos &#952; 1 r 1 2 . Electric potential at any general point for  V 2 &#8733; p 2 cos &#952; 2 r 2 2 . For first case:  tan &#952; 1 = 100 100 = 1 &#8658; &#952; 1 = 45 &#176; For second case: slope in this is  = - 2 - 2 1 - - 1 = - 2 which is equal to  tan 45 &#176; + &#952; 2 = - 2 &#8658; 1 + tan &#952; 2 1 - tan &#952; 2 = - 2 &#8658; 1 + tan &#952; 2 = - 2 + 2 tan &#952; 2 &#8658; tan &#952; 2 = 3 cos &#952; 2 = 1 3 2 + 1 2 = 1 10 also  r 1 = r 2 . Therefore, required ratio V 2 V 1 = p 2 cos &#952; 2 p 1 cos &#952; 1 V 2 V 1 = q l 2 &#215; 1 10 q l 1 &#215; 1 2 = 2 - - 2 2 + - 1 - 1 2 4 &#215; 5 = 2 5 4 &#215; 5 = 1 2 &#8658; &#160; V 2 = V 0 2

JEE Advanced Physics Question (2023) — Solution

Question

Options

Answer

Step-by-step solution