question_answer

The electric intensity due to a dipole of length 10 cm and having a charge of \[500\,\mu C,\] at a point on the axis at a distance 20 cm from one of the charges in air, is

A) \[6.25\times {{10}^{7}}\,N/C\] 

B) \[9.28\times {{10}^{7}}\,N/C\]

C) \[13.1\times {{11}^{11}}\,N/C\]

D) \[20.5\times {{10}^{7}}\,N/C\]   

Correct Answer: A

Solution :

 By using \[E=9\times {{10}^{9}}.\frac{2pr}{{{({{r}^{2}}-{{l}^{2}})}^{2}}}\] Where\[p=(500\times {{10}^{-6}})\times (10\times {{10}^{-2}})=5\times {{10}^{-5}}\,c\times m,\] \[r=25cm=0.25\,m,\,l=5\,cm=0.05\,m\] \[E=\frac{9\times {{10}^{9}}\times 2\times 5\times {{10}^{-5}}\times 0.25}{{{\{{{(0.25)}^{2}}-{{(0.05)}^{2}}\}}^{\,2}}}\] \[=6.25\times {{10}^{7}}\,N/C\]