Question

# A charge of magnitude Q is placed at the origin. A second identical charge is placed at the position x=d along the x-axis. Other than infinitely far away, at what position on the x-axis will a positive test charge experience a zero net force?

A
x=d
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B
x=d2
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C
x=d2
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D
x=3d2
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E
Cannot be determined from the given information
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Solution

## The correct option is C x=d2Let the electric field E is zero at a point P between the two given charges , at a distance x from the charge Q which is at the origin .at point P, electric field due to Q at origin E1=KQx2at point P, electric field due to Q at a distance d from Q at origin E2=KQ(d−x)2as E1 and E2 are in opposite direction due to two positive charges and electric field is zero at point P , therefore E1=E2or KQx2=KQ(d−x)2or x2=(d−x)2or x=d2 or 3d2 but x=3d2 is not possible as point P is in between the two charges .now if we put a positive test charge q at point P , force on it F=qE=q×0=0option C is correct .

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