Electromagnetic Oscillations And Alternating Current

The accurate matching of physics rules with their statements is:

Detailed Explanation:

• Ampere Swimming Rule (A → III):

This rule describes the deflection of a magnetic needle near a current-carrying conductor. If a swimmer swims in the direction of current, the north pole of a magnetic needle will deflect toward their left hand.

• Fleming's Left Hand Rule (B → IV):

Used to determine the direction of force on a current-carrying conductor placed in a magnetic field (Thumb = Thrust/Force, Forefinger = Magnetic Field, Middle finger = Current direction).

• Fleming's Right Hand Rule (C → I):

Used to find the direction of induced current when a conductor moves through a magnetic field (Thumb = Motion, Forefinger = Magnetic Field, Middle finger = Induced Current).

• Right Hand Thumb Rule (D → II):

Also called Maxwell's corkscrew rule, determines the direction of magnetic field lines around a current-carrying conductor (thumb points in current direction, curled fingers show field direction).

Final Correct Matching:

• A → III (Ampere Swimming Rule for magnetic needle deflection)
• B → IV (Fleming's Left Hand Rule for force direction)
• C → I (Fleming's Right Hand Rule for induced current)
• D → II (Right Hand Thumb Rule for magnetic field direction)

When two identical coaxial coils P and Q are carrying equal currents in the same direction and are brought closer together, they interact through their magnetic fields. The principle at play here is Lenz's Law, which states that the direction of the induced electromotive force (emf) is such that it opposes the change in magnetic flux that produced it.

As the coils are brought closer, the magnetic flux linkage through each coil increases due to the presence of the other's magnetic field. To oppose this increase in magnetic flux, the system will act to reduce the current flowing in each coil. This is due to Lenz's Law, which effectively reduces the magnetic interaction by decreasing the currents.

The correct choice, in this scenario, is that both P and Q decrease in current. This is consistent with induced electromagnetic effects seeking to counteract changes in their magnetic environment:

• The mutual inductance between the coils increases as they approach each other.
• This increased mutual inductance results in a greater opposing emf, reducing the net current in each coil.

Therefore, when such an interaction occurs, the result is both P and Q experience a decrease in current.

The electromagnetic spectrum is ordered by frequency (and inversely by wavelength). The order from lowest to highest frequency is:

1. Radio waves
2. Microwaves
3. Infrared
4. Visible light
5. Ultraviolet
6. X-rays
7. Gamma rays

Therefore, we can arrange the given frequencies in ascending order:

Answer:

To find the magnetic field at point P, we analyze the contributions from all current-carrying segments:

1. Segment AB: The current flows from A to B. Using the Biot-Savart law, the magnetic field at P (distance r away) would be: (direction into the page)

2. Segment BC: Since P lies along the collinear extension of BC (C'B'PBC are collinear), the current element and displacement vector are parallel. From Biot-Savart law: because θ = 0° ⇒ sinθ = 0. Thus, .

3. Segment APSC: The current flows in the opposite direction (S to A). The magnetic field contribution at P would be: (direction out of the page, opposite to B_AB)

The total magnetic field at P is the sum of these contributions:

Final answer: The magnetic field at P is (Option 4).