- #1

sebah

- 5

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I know that the electric field strength at point P is ##E=150 \frac{V}{m}##, ##d=1.8m## and ##a=2.5m##. I want to find the charge of ##Q##. As far as I know, the electric field on the y-axis between the two charges is given by:

$$E=\frac{2xQ}{4 \pi \epsilon_0 (x^2+y^2)^{\frac{3}{2}}}$$

where ##x## is the distance between one charge and the origin and ##y## is the distance from the origin on the ##y##-axis. In this case ##y=d## and ##x=\frac{a}{2}##.

$$E=\frac{aQ}{4 \pi \epsilon_0 ((\frac{a}{2})^2+d^2)^{\frac{3}{2}}}$$

Solving for ##Q##:

$$Q=\frac{E 4 \pi \epsilon_0 ((\frac{a}{2})^2+d^2)^{\frac{3}{2}}}{a}$$

Plugging in values gives me:

$$Q=7.02 \cdot 10^{-8} C=70nC$$

The correct answer is supposed to be ##~50nC=50\cdot 10^{-9}C##. Am I doing something wrong or is there a mistake in the solution?