Inductance

Magnetic field B

Step 1: Understanding the formula for resonant frequency. The resonant frequency of an LC oscillator is given by: where: - is the inductance, - is the capacitance.
Step 2: Initial resonant frequency.
Step 3: New resonant frequency after changes. Given: - , - , the new resonant frequency is:
Step 4: Finding . Since , we get:
Final Answer:

Step 1: {Define self-inductance}
The energy stored in an inductor is given by: where is the self-inductance and is the current.
Step 2: {Rearrange for }

Step 3: {Find the dimensional formula of }
Since energy ( ) has the dimensional formula: and current ( ) has the dimensional formula: we substitute:
Step 4: {Verify the options}
Comparing with the given choices,
the correct answer is (A) .