A charge Q = - 845 nC is uniformly distributed on a ring of 2.2 m radius. A char
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A charge Q = - 845 nC is uniformly distributed on a ring of 2.2 m radius. A charge q=+532 nC is placed at the center of the ring. Points A and B are located on the axis of the ring, as shown. In Figure, the work in eV (as a whole number) done by an external force that transports an electron from B to A is:
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A charge Q = - 845 nC is uniformly distributed on a ring of 2.2 m radius. A charge q=+532 nC is placed at the center of the ring. Points A and B are located on the axis of the ring, as shown. In Figure, the work in eV (as a whole number) done by an external force that transports an electron from B to A is:Explanation / Answer
Let the central axes be the z-axes. Then we need the electric field at every point on that axes, because the we can calculate the work as
W = - q integral E_z(z) dz
The E-field z-component along the axes has two contributions. That from the single charge +q is
E = k Q / z^2
and that from the ring of charge -Q.
Each point on the ring has distance d to point z given by
d^2 = R^2 + z^2
The component of the field at z in the direction of the axis has an additional geometrical factor z/d. So for the second contribution we have
E = - kQ * z/d^3
= -k Q z/(z^2 + R^2)^(3/2)
Therefore the total electrical fieldstrength in the direction of z is
E = k q/ z^2 - kQ z/(z^2+R^2)^(3/2)
To calculate the work, integrate this between the z-values given and multiply with -(-e).
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