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?

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Solution

The correct option is **C** x=d2

Let 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 .

Let 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=KQx2

at point P, electric field due to Q at a distance d from Q at origin

E2=KQ(d−x)2

as E1 and E2 are in opposite direction due to two positive charges and electric field is zero at point P , therefore

E1=E2

or KQx2=KQ(d−x)2

or x2=(d−x)2

or 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=0

option C is correct .

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