Modern Physics

Step 1: Understanding the Magnetic Field Distribution
The magnetic field around a current
carrying wire is given by Ampère's Circuital Law: where is the current enclosed by the chosen circular Amperian loop.
Step 2: Magnetic Field Inside the Wire ( )
Since the current is uniformly distributed, the enclosed current at a radius (where ) is: Applying Ampère’s law for a circular path of radius : Substituting : This shows that the magnetic field inside the wire is directly proportional to .
Step 3: Magnetic Field Outside the Wire ( )
For , the entire current is enclosed within the Amperian loop: Thus, the magnetic field outside the wire is inversely proportional to . Final Answer:
The magnetic field inside the wire is directly proportional to , and outside the wire, it is inversely proportional to .

Step 1: Understanding the Magnetic Field Distribution
The magnetic field around a current
carrying wire is given by Ampère's Circuital Law: where is the current enclosed by the chosen circular Amperian loop.
Step 2: Magnetic Field Inside the Wire ( )
Since the current is uniformly distributed, the enclosed current at a radius (where ) is: Applying Ampère’s law for a circular path of radius : Substituting : This shows that the magnetic field inside the wire is directly proportional to .
Step 3: Magnetic Field Outside the Wire ( )
For , the entire current is enclosed within the Amperian loop: Thus, the magnetic field outside the wire is inversely proportional to . Final Answer:
The magnetic field inside the wire is directly proportional to , and outside the wire, it is inversely proportional to .

Step 1: Understanding the Problem
We are given four resistances: , , , and . We need to connect them in such a way that the equivalent resistance is .
Step 2: Analyzing the Options
We will evaluate each option to see which configuration gives the desired equivalent resistance.
Step 3: Evaluating Option (A)
In option (A), and are in parallel, and and are in series.
First, calculate the equivalent resistance of and in parallel:
Next, calculate the equivalent resistance of and in series:
Now, combine the parallel and series resistances:
This does not match the desired equivalent resistance of . Therefore, option (A) is incorrect.
Step 4: Evaluating Option (B)
In option (B), and are in parallel, and and are in series.
First, calculate the equivalent resistance of and in parallel:
Next, calculate the equivalent resistance of and in series:
Now, combine the parallel and series resistances:
This does not match the desired equivalent resistance of . Therefore, option (B) is incorrect.
Step 5: Evaluating Option (C)
In option (C), and are in parallel, and and are in series.
First, calculate the equivalent resistance of and in parallel:
Next, calculate the equivalent resistance of and in series:
Now, combine the parallel and series resistances:
This does not match the desired equivalent resistance of . Therefore, option (C) is incorrect.
Step 6: Evaluating Option (D)
In option (D), and are in parallel, and and are in series.
First, calculate the equivalent resistance of and in parallel:
Next, calculate the equivalent resistance of and in series:
Now, combine the parallel and series resistances:
This matches the desired equivalent resistance of . Therefore, option (D) is correct. Final Answer: The correct configuration is (D) and are in parallel with and in series.

Step 1: Use the relation between energy and frequency The energy of a photon is given by: Where: - - Step 2: Rearrange to find frequency Answer: The frequency of the photon is . Hence, the correct answer is option (1).