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An infinite number of charges each numer...

An infinite number of charges each numerically equal to q and of the same sign are placed along the x-axis at `x = 1, x = 2, x = 4, x = 8` and so on. Find electric potential at `x=0`.

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AI Generated Solution

To find the electric potential at \( x = 0 \) due to an infinite number of charges placed along the x-axis at positions \( x = 1, 2, 4, 8, \ldots \), we can follow these steps: ### Step 1: Understand the Electric Potential Formula The electric potential \( V \) due to a point charge \( q \) at a distance \( r \) is given by the formula: \[ V = \frac{1}{4 \pi \epsilon_0} \frac{q}{r} \] where \( \epsilon_0 \) is the permittivity of free space. ...
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Knowledge Check

  • An infinite number of charges , each equal to q , are placed along the x - axis at x = 1, x=2,x=4,x=8 and so on . The potential at x = 0 due to this set of charges is

    A
    `(4q)/(2piepsilon_(0))`
    B
    `2q//4piepsilon_(0)`
    C
    `(q)/(2piepsilon_(0))`
    D
    `(2q)/(piepsilon_(0))`
  • An infinite number of electric charges each equal to 5 nano-coulomb (magnitude) are placed along X -axis at x=1 cm, x=2 cm,x=8cm ……and so on. In the setup if the consecutive charges have opposite sign, then the electrical field in Newton/Coulomb at x=0 is (1/(4piepsilon_(0))= 9xx10^(9)N-m^(2)//C^(2))

    A
    `12xx10^(4)`
    B
    `24xx10^(4)`
    C
    `36xx10^(4)`
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    `48xx10^(4)`
  • An infinite number of charges, each of magnitude q, are placed along x-axis at x = 1m, 2m, 4m, 8m, 16m and so on but the consecutive charges are of opposite sign starting with +q at x = 1m. A point charge q_0 , kept at the origin, experiences a force of magnitude :

    A
    `(qq_0)/(4 pi epsi_0)`
    B
    `(qq_0)/(5 pi epsi_(0))`
    C
    `(qq_(0))/(3pi epsi_0)`
    D
    `(qq_(0))/(2piepsi_(0))`
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