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Question

A charge $$Q$$ is placed at each of the opposite corners of a sequare. A charge $$q$$ is placed at each of the other two corners. If the net electric force on $$Q$$ is zero, then $$Q/q$$ equals:


A
1
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B
1
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C
12
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D
22
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Solution

The correct option is D $$-2\sqrt {2}$$

$$\dfrac { Q }{ q } =-2\sqrt { 2 } $$
$${ F }_{ net }$$ on $$q={ \overline { F }  }_{ 1 }+{ \overline { F }  }_{ 2 }+{ \overline { F }  }_{ 3 }$$
$$0=F\hat { i } +F\hat { j } +{ \overline { F }  }_{ 3 }$$
$$0=\dfrac { { K }_{ q }Q }{ { a }^{ 2 } } \left( \hat { i } +\hat { j }  \right) +\dfrac { { Kq }^{ 2 } }{ { \left( \sqrt { 2 } a \right)  }^{ 2 } } \dfrac { \hat { i } +\hat { j }  }{ \sqrt { 2 }  } $$
$$0=\left( \dfrac { { K }_{ q }Q }{ { a }^{ 2 } } +\dfrac { { K }_{ q }Q }{ 2\sqrt { 2 } { a }^{ 2 } } \left( i+j \right)  \right) $$
$$qQ+\dfrac { { a }^{ 2 } }{ 2\sqrt { 2 }  } =0$$
$$q=-2\sqrt { 2 } Q$$

1238493_1135344_ans_03ec8b4755ef4b91aa87fb9b02cf8db6.jpg

Physics

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