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Q.

An infinite number of electric charges each equal to 5 nC (magnitude) are placed along x-axis at x =1 cm, x = 2 cm, x = 4 cm, x = 8m .......... and so on. In the setup, if the consecutive charges have opposite sign, then the electric field in newton/coulomb at x = 0 is 14πε0=9×109N−m2/C2

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a

12×104

b

24×104

c

36×104

d

48×104

answer is C.

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Detailed Solution

E=14πε0⋅5×10−91×10−22−5×10−92×10−22+5×10−94×10−22−5×10−98×10−22+….. ⇒E=9×109×5×10−910−41−1(2)2+1(4)2−1(8)2+… ⇒E=45×1041+1(4)2+1(16)2+…−45×1041(2)2+1(8)2+1(32)2+… ⇒E=45×10411−116−45×104(2)21+142+1(16)2+.. E=48×104−12×104=36×104N/C

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An infinite number of electric charges each equal to 5 nC (magnitude) are placed along x-axis at x =1 cm, x = 2 cm, x = 4 cm, x = 8m .......... and so on. In the setup, if the consecutive charges have opposite sign, then the electric field in newton/coulomb at x = 0 is 14πε0=9×109N−m2/C2