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Question

Two electric charges $$2q$$ and $$8q$$ are placed at a distance of $$6a$$ on a horizontal plane. The distance of the location of the point from charge $$2q$$ where the electric field is zero is


A
2a
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B
a
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C
1.5a
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D
2.5a
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Solution

The correct option is A $$2a$$

Given 2 charges $$2q$$ & $$ 8q$$ are pleased at a distance of $$6a$$ on a horizontal plan.

suppose $$+ve$$ charge $$+2q$$ is placed at origin and charge $$+8q$$ is placed at (6a,0).

Let point p on the$$ x$$-axis at the distance $$ "x"$$ from the origin when the electric field is zero.

 Electric field at P due to Chang 2q

$${ E }_{ 1 }=k.\cfrac { 2q }{ { x }^{ 2 } } $$

Electric field at P due to Chang 8q

$${ E }_{ 2 }=k.\cfrac { 8q }{ { \left( 6a-x \right)  }^{ 2 } }$$

the net electric to be zero

means $${ E }_{ 1 }={ E }_{ 2 }$$

 ie,

$$ k.\cfrac { 2q }{ { x }^{ 2 } } =k.\cfrac { 8q }{ { \left( 6a-x \right)  }^{ 2 } } \\ \Rightarrow { \left( 6a-x \right)  }^{ 2 }=4{ x }^{ 2 }$$

 Taking square root on both sides

$$ 6a-x=2x\\ 6a=3x\\ x=2a\\ so,$$

 the answer is option (a).


Physics
NCERT
Standard XII

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