  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  B
a  C
1.5a  D
2.5a  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 zeromeans $${ E }_{ 1 }={ E }_{ 2 }$$ 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).PhysicsNCERTStandard XII

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