If the net electric field at point P along Y axis is zero, then the ratio of | q2/ q3 | is 8 / 5√ x ,

Question

If the net electric field at point \(\mathrm{P}\) along \(\mathrm{Y}\) axis is zero, then the ratio of \(\left|\frac{\mathrm{q}_{2}}{\mathrm{q}_{3}}\right|\) is \(\frac{8}{5 \sqrt{\mathrm{x}}}\),

where  \(\mathrm{x}=\) ..............

Answer 1

Correct answer is : 5 

\(\frac{\mathrm{Kq}_{2}}{20} \cos \beta=\frac{\mathrm{Kq}_{3}}{25} \cos \theta\)

\(\frac{\mathrm{Kq}_{2}}{20} \frac{4}{\sqrt{20}}=\frac{\mathrm{Kq}_{3}}{25} \frac{4}{\sqrt{25}}\)

\(\frac{\mathrm{q}_{2}}{\mathrm{q}_{3}}=\frac{20}{25} \sqrt{\frac{20}{25}}=\frac{8}{5 \sqrt{\mathrm{x}}}\)

\(\Rightarrow \sqrt{\mathrm{x}}=\frac{8 \times 25 \sqrt{25}}{5 \times 20 \sqrt{20}}\)

\(\mathrm{x}=5\)