Displacement Current

Step 1: Recall the Energy Densities

The average electric energy density ( ) and the average magnetic energy density ( ) of an electromagnetic wave are equal: The total average energy density ( ) is the sum of the electric and magnetic energy densities:

Step 2: Find the Ratio

Since , we have: Thus: The ratio of average electric energy density to the total average energy density is:

Conclusion: The ratio is (Option 3).

The problem involves a rectangular loop PQRS made of a uniform wire with current flowing through it. We need to find the ratio of the magnetic forces per unit length on the wire PQ due to the change in current.

Given: - Length - Length
The current changes from to .
We are asked to find the ratio of magnetic forces per unit length on the wire PQ in the two cases, denoted as and , respectively.

Magnetic Force Formula: The magnetic force per unit length on a straight current-carrying conductor in a magnetic field is given by the formula: Where:
is the magnetic field strength,
is the current,
is the length of the wire in the magnetic field.

Step 1: Magnetic field due to the current on the wire PQ can be calculated using Ampere's law, but since the wire is rectangular and the length of the segments PR and QS are equal, we focus on the effect of current in the longer segments PQ and RS.

Step 2: Since the current increases from to , the magnetic force will change quadratically with the current, as shown by the relation: This is because force is proportional to the square of the current, i.e., .

Step 3: Therefore, the ratio of the magnetic forces per unit length on the wire PQ due to the current and is:

The correct answer is: (D): 1:4