Tuesday, February 07, 2006

Charging by Induction

Placing a Charge on a Conductor without touching it

Two uncharged metal balls, X and Y, stand on an insulating mat. A third ball, Z, carrying a positive charge, is brought near X and Y:
    (X) (Y) (Z)+

Then, a conducting wire is placed so it connects X and Y.

    (X)--------(Y) (Z)+
After a few minutes, the wire is removed, and then Z is taken far away from X and Y.

When this is done, it is found that:

    a) balls X and Y are positively charged

    b) balls X and Y are still uncharged

    c) balls X and Y are both negatively charged

    d) ball X is positively charged and ball Y is negatively charged

    e) ball Y is positively charged and ball X is negatively charged

The answer is d.

As Z comes towards the pair of balls, the electrons in both balls are attracted towards Z. Being held within the metal, this means they congregate at the right hand side of the two spheres. At this point, the two spheres still have an overall neutral charge, but the charge is distributed unevenly upon it – the right hand sides are negative and the left hand sides are positive:

    +(X)- +(Y)- +(Z)

The wire then joins the negative side of X to the positive side of Y, allowing the electrons on X to move closer to Z (and the positive ions left on the left hand side of Y). To a good approximation, after a short time, the charges are distributed thusly:

    ++(X)-----------(Y)-- +(Z)
Once the wire is removed, the electrons are unable to move back to where they came from:

    ++(X) (Y)-- +(Z)
Removing Z reduces the forces making the charges separate (although the charges on X and Y also affect each other) so the two balls are left roughly like: +(X)+ -(Y)-

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