A charge Q = - 822 nC is uniformly distributed on a ring of 1.9 m radius. A char
ID: 2128103 • Letter: A
Question
A charge Q = - 822 nC is uniformly distributed on a ring of 1.9 m radius. A charge q=+537 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:
A charge Q = - 822 nC is uniformly distributed on a ring of 1.9 m radius. A charge q=+537 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
The distance from any part of the ring (radius R) to the point on x-axis is sqrt(R^2 + x^2) (Pythagoras)
The potential at x from a charge element dQ is kdq/d = kdQ/sqrt(R^2 + x^2)
Since all charge elements are the same distance from the point on the axis, and potentials are scalars (no direction components to consider, then:
Total potential at x = Integral[kdQ/sqrt(R^2 + x^2)] = kQ/sqrt(R^2 + x^2) + C
By taking V=0 when x =infinity, we get C=0
Potential due to ring when x=2m = (9x10^9) x (3x10^-9) / sqrt(0.1^2 + 2^2) = 13.483V
Potential due to ring when x=0m = (9x10^9) x (3x10^-9) / sqrt(0.1^2 + 0^2) = 2700V
Potential difference, deltaV = 2700 - 13.483 = 2687V *rounded)
Work done = q x deltaV = 1x10^-9 x 2687 = 2.7x10^-6J (rounded to 2 sig. figs)
To convert to eV divide by 1.6x10^-19 to give 1.7x10^13eV
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