Two charges +6μC and −4μC are placed 15cm apart as shown. At what distances from A to its right, the electrostatic potential is zero?
4,9,60
9,15,45
20,30,40
9,45, infinity
A
4,9,60
B
9,45, infinity
C
9,15,45
D
20,30,40
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Solution
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Let the potential be zero at point P at a distance x from the
charge +6×10−6C at A as shown in above figure.
Potential at P V=14πε0[6×10−6x−(−4×10−6)15−x] 0=14πε0[6×10−6x−4×10−615−x] 0=6×10−6x−4×10−615−x 6×10−6x=4×10−615−x ⇒6(15−x)=4x ⇒90−6x=4x ⇒10x=90 ⇒x=9010=9cm The
other possibility is that point of zero potential P may lie on
AB produced at a distance x from the charge +6×10−6C at A as shown in the figure. Potential at P V=14πε0[6×10−6x+(−4×10−6)(15−x)] 0=14πε0[6×10−6x−4×10−6(x−15)] 0=6×10−6x−4×10−6(x−15) ⇒6×10−6x=4×10−6x−15 ⇒6x=4x−15 ⇒6x−90=4x ⇒2x=90 ⇒x=902=45cm
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