Question

For an electric dipole \( |\vec{P}| \hat{i} \) at origin, find the value of ' \( \tan \delta \) ' at point \( A(3,4) \). Here ' \( \delta \) ' is the angle made by resulting electric field at point \( A \) with +ve \( x \)-axis.

Answer 1

\(\theta = tan^{-1}(4/3)\) 

\(\theta=53.13^o\)

\(\vec E = \frac{KP}{r^3}\)[2 cos θ \(\hat r\) + sin θ \(\hat {\theta}\) ]

E₁ = \(\frac{2KP}{r^3}cos\theta\) 

E₁ = \(\frac{2KP}{r^3}(\frac35)\) 

E₂ = \(\frac{KP}{r^3}sin\theta\) 

E₂ = \(\frac{KP}{r^3}(\frac45)\) 

\(\frac{E_2}{E_1}=\frac{4/5}{6/5}\)

\(\frac{E_2}{E_1}=\frac46\) ⇒ \(\frac23\) 

α = tan^-1(\(\frac{E_2}{E_1}\))

α = tan^-1(2/3)

\(\delta\) = θ + α

\(\delta\) = tan^-1(4/3) + tan^-1(2/3)

\(\delta\) = tan^-1(4/3) + tan^-1(2/3)

\(\delta\) = tan^-1\(\left[\cfrac{\frac43+\frac23}{1-\frac43\times\frac23}\right]\) 

tan \(\delta\) = 6/-5