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 [CBSE PMT 2001]

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 \[E=9\times {{10}^{9}}.\frac{2p\,r}{{{({{r}^{2}}-{{l}^{2}})}^{2}}};\] where \[p=(\text{5}00\times \text{1}{{0}^{\text{6}}})\times (\text{1}0\times \text{1}{{0}^{\text{2}}})=\text{5}\times \text{1}{{0}^{\text{5}}}\], r = 25 cm = 0.25 m, l = 5 cm = 0.05 m \[E=\frac{9\times {{10}^{9}}\times 2\times 5\times {{10}^{-5}}\times 0.25}{{{\{{{(0.25)}^{2}}-{{(0.05)}^{2}}\}}^{2}}}\] \[=6.25\times {{10}^{7}}N/C\]