Introduction:
When an electric current passes through a solid conductor, it results in the flow of charged particles, typically electrons. The electric current density is a measure of the amount of electric current flowing through a unit cross-sectional area of the conductor.

Given Information:
- Electric current is passing through a solid conductor PQ from P to Q.
- The electric current densities at P and Q are in a certain ratio.

Understanding Electric Current Density:
Electric current density (J) is defined as the amount of electric current (I) flowing per unit cross-sectional area (A) of the conductor. Mathematically, it can be expressed as J = I/A.

Analysis:
Let's assume that the electric current density at point P is Jp, and the electric current density at point Q is Jq. We are given that Jp : Jq = ?

We know that the current passing through any cross-section of the conductor is constant, as it is a continuous flow of charge. Therefore, the electric current at point P (Ip) is equal to the electric current at point Q (Iq).

Since I = J * A, where A is the cross-sectional area of the conductor, we can write Ip = Jp * Ap and Iq = Jq * Aq.

Since Ip = Iq, we can equate the expressions:
Jp * Ap = Jq * Aq

Solution:
To find the ratio of Jp to Jq, we need to determine the ratio of Ap to Aq.

Conclusion:
Based on the given information and analysis, the ratio of electric current densities at points P and Q depends on the ratio of the cross-sectional areas of the conductor at those points. Without information about the cross-sectional areas, we cannot determine the exact ratio of the electric current densities. Therefore, the answer cannot be determined with the given information.

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