Electromagnetic Induction

To solve the problem, we need to identify the correct physical principle behind the operation of a metal detector.

1. Understanding Metal Detectors:
Metal detectors typically use a coil of wire through which an alternating current is passed. This generates a time-varying magnetic field. When a metal object is present nearby, it alters this magnetic field, often by inducing eddy currents in the metal. These eddy currents, in turn, produce their own magnetic fields, which can be detected by the sensor.

2. Relevant Principle:
This behavior is governed by Faraday’s Law of Electromagnetic Induction, which states that a changing magnetic field induces an electromotive force (EMF) in a conductor. The principle of electromagnetic induction is what allows metal detectors to sense nearby conductive objects.

3. Eliminating Incorrect Options:
- Ohm’s law relates voltage, current, and resistance: not relevant here.
- Coulomb’s law describes electrostatic force: not related to detection of metals.
- Stefan’s law relates to blackbody radiation: not applicable in this context.
- Electromagnetic induction: correct, as it is the working principle behind how metal detectors detect metal objects.

Final Answer:
Metal detectors work on the principle of Electromagnetic Induction.

To solve the problem, we need to analyze the behavior of the given AC circuit at very high frequencies and determine the current flowing through it.

1. Behavior of Components at High Frequencies:
At very high frequencies: - Inductive reactance (inductors behave like open circuits) - Capacitive reactance (capacitors behave like short circuits)

2. Analyzing the Circuit:
Given these behaviors: - All inductors (20 mH, 50 mH) will act as open circuits and hence block current in their branches. - All capacitors (0.8 µF, 0.5 µF) will act as short circuits and can be replaced with wires.
With inductors acting as open circuits, the paths containing them become irrelevant for current flow. Therefore, current only flows through the branches that have only resistors and shorted capacitors**.

3. Remaining Effective Circuit:
After simplification: - The remaining path includes: 220V source → 1Ω resistor → shorted capacitors (negligible resistance) → 4Ω resistor → total resistance = 5Ω.

4. Calculating Current:
Using Ohm's law:

Final Answer:
The current in the circuit at very high frequencies is 44 A.

To solve the problem, we need to calculate the EMF induced across the radius of a rotating copper disc in a transverse magnetic field.

1. Understanding the Concept:
The EMF induced across the radius of a rotating disc in a uniform magnetic field is given by the formula:

Where:
- is the magnetic field strength,
- is the angular velocity in radians per second,
- is the radius of the disc.

2. Given Values:
-
-
- Revolutions per second = 10
- So, angular velocity:

3. Substituting into the Formula:

4. Converting to millivolts:

Final Answer:
The EMF induced across the radius of the disc is mV.

Step 1: Formula for Energy Stored:
The energy stored in an inductor is given by .

Step 2: Calculate New Energy:
Let initial current be . New current increases by : $ U' $
Step 4: Final Answer:
The percentage increase in energy is 44\%.