Question

Two point charges are placed at a and b at a certain distance from each other. Assuming the field strength is positive in the direction coinciding with the positive direction of the x axis ($l_1 > l_2$):

• A. Charge at a is positive and at b negative
• B. Magnitude of charge at a is greater than that of charge at b
• C. Both charges at a and b are negative
• D. Magnitude of charge at b is greater than that of charge at a

Answer 1

Answer: (A), (B)

Options (A) and (B)

Answer 2

We note that the net field along the line never reverses its (positive‐x) sense but shows a “dip” in magnitude. This “minimum” (not zero) occurs when one charge gives a field that decreases while the other’s increases as we change position. It turns out that if one charge is positive and the other negative then, for all points between (and even outside) the two charges, both fields can “point” in the same (here “+x”) direction. In the usual arrangement, if we choose the left charge (say at “a”) to be positive then its field points away from it (i.e. to the right for the region between the charges) while the right charge (at “b”) being negative produces a field that points toward it (again to the right on its left side).

Moreover, the graph shows that the “singularity” (rapid increase) in the field strength occurs near the dashed line marked by $l_2$ (the projection of charge b) while the field near charge a (with projection $l_1$) is less steep. Since $l_1>l_2$ the minimum lies closer to b. In a system of two unequal charges of opposite sign the dip in net field lies nearer the weaker charge. Hence the charge at b must have a smaller magnitude than that at a.

Thus the correct inferences are:

• Charge at a is positive and at b is negative.
• The magnitude of the charge at a is greater than that of b.