A charge q and a charge -q are placed at opposite corners of a square. Will a third point charge experience a greater force if it is placed at one of the empty corners of the square, or at the center of the square?

Respuesta :

Answer:

Explanation:

Given

two point charges q and -q are placed at corner of square

suppose a is the side length of square

If a charge [tex]q_2[/tex] is placed at a one of the corner then Force on it due to +q

[tex]F_{+q}=\frac{kqq_2}{a^2}[/tex]

Force on [tex]q_2[/tex] due to -q is given by

[tex]F_{-q}=\frac{-kqq_2}{a^2}[/tex]

Net force [tex]F_{net}=\sqrt{(F_{+q})^2+(F_{-q})^2}[/tex]

[tex]F_{net}=\sqrt{2}\frac{kqq_2}{a^2}[/tex]

When charge is placed at center then distance between  charges becomes [tex]\frac{\sqrt{2}}{2}=\frac{a}{\sqrt{2}}[/tex]

One charge will cause [tex]q_2[/tex] to move away from it while other attracts it

[tex]F'_{net}=2\times \frac{kqq_2}{(\frac{a}{\sqrt{2}})^2}[/tex]

[tex]F'_{net}=2\times 2\times \frac{kqq_2}{a^2}[/tex]

[tex]F'_{net}=4\frac{kqq_2}{a^2}[/tex]

Therefore When charge is Placed at center then it experience more force

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