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A charge of 8 mC is located at the orig...

A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of `-2xx10^(-9)C` from a point P (0,0,3 cm) to a point Q (0,4 cm, 0) via a point R (0,6 cm, 9cm).

Text Solution

Verified by Experts

Work done in moving the charge from one point to another in an external field is independent of the path and depends only on the initial and final points, so mentioning point R in the question is of no use.

charge fixed at origin, `q=8xx10^(-3)C`
Charge to be moved, `q.=-2xx10^(-9)C`
From the figure we can find:
Distance of point P from origin, `r_(P)=3xx10^(-2)m`
Distance of point Q from origin, `r_(Q)=4xx10^(-2)m`

Work done can be calculated as
`W=q.(V_(Q)-V_(P))`
`W=(qq.)/(4pi epsilon_(0))[(1)/(r_(Q))-(1)/(r_(P))]`
`W=9xx10^(9)xx8xx10^(-3)xx(-2xx10^(-9))xx [(1)/(4xx10^(-2))-(1)/(3xx10^(-2))]`
`=1.2J`
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A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of -2 xx 10^(-9)C from a point P(0,0,3 cm) to a point Q10,4 cm, 0) via a point R(0,6 cm, 9 cm).

A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of -2xx10^(-9) from a point P(0,0,3cm) to a point Q (0,4cm,0) via a point R(0,6cm,9cm).

Knowledge Check

  • Calculate the work done in taking a charge - 2 xx 10^(-9) C from A to B via C (in diagram )

    A
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    B
    1.2 joule
    C
    2.2 joule
    D
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  • As per this diagram a point charge +q is placed at the origin O . Work done in taking another point charge -Q from the point A(0, a) to another point B(a, 0) along the staight path AB is:

    A
    `((-qQ)/(4pi epsilon_(0))(1)/(a^(2)))sqrt(2a)`
    B
    zero
    C
    `((qQ)/(4pi epsilon_(0))(1)/(a^(2)))(1)/sqrt(2)`
    D
    `((qQ)/(4pi epsilon_(0))(1)/(a^(2)))(1)/sqrt(2a)`

  • As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge -q from the point A[co-ordinates (0,a)] to another point B[co-ordiantes (a,0)] along the straight path AB is

    A
    zero
    B
    `(-qQ//4pi epsi 0) (1//a2) sqrt""2a`
    C
    `(qQ//4pi epsi 0) (1//a2) .a//sqrt""2`
    D
    `(qQ//4pi epsi 0) (1//a2) sqrt""2a`

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