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Electric Field & Magnitudes

The lines show the equipotential contours in the plane of three point charges, Q1, Q2, and Q3. The values of the potentials are in kV as indicated for the +5, 0, and -5 kV contours. The positions of the charges are indicated by the dots.

the work required to move a charge of -0.51×10-12C from i to b is 3.06×10-9 J

a: Calculate the size of the electric field at k.

b: Calculate the size of the force on a charge of 8.00×10-19 C at g.

c: Calculate the size of Q3. The magnitudes of the three charges are in the exact ratios of 1 to 2 to 3.

Solution Preview

The electric potential due to a point charge is V = kQ/r and therefore close to a charge the potential (V ) will have the same sign as the charge (Q) and the magnitude will be large due to small r. From this we know that Q1 and Q2 are negative while Q3 is positive. Note that there are equipotential lines with a magnitude of 5 kV around each of the charges. Since |V | is the same for each, this means Q/r must be the same. Therefore, a charge that has a larger r must have a larger Q. Therefore, Q3 has the largest magnitude charge since the distance to the |V | = 5 kV line is greatest. Also, Q1 is the largest negative charge since Q3 is positive.
At point k the electric ...

Solution Summary

This solution contains step-by-step calculations and in-depth explanations to determine the size of electric field, size of force and size of Q3 using equations for electric field with equipotential lines, electric field force and charge.

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