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
B
1
C
12
D
22

Solution

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

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