Faradays Laws Of Induction

Step 1: Understand the problem.
A conducting wire is moving towards the right in a magnetic field, and there is an induced current in the wire. We need to determine the direction of the magnetic field.

Step 2: Apply Fleming’s Right-Hand Rule.
Fleming’s Right-Hand Rule states that if the thumb, index, and middle fingers of the right hand are held mutually perpendicular to each other, then: - The thumb represents the direction of motion of the conductor (velocity ). - The index finger represents the direction of the magnetic field . - The middle finger represents the direction of the induced current. Here, the wire moves towards the right ( towards the right) and the current is shown to go in the direction to the right. Applying the rule, the magnetic field must be perpendicular to the paper and directed downwards.

Step 3: Conclusion.
Therefore, the direction of the magnetic field will be perpendicular to the plane of the paper and downwards.

Step 1: Understand the formula for induced emf.
The induced emf in a coil due to a changing magnetic field is given by Faraday's law of electromagnetic induction: where is the magnetic flux, is the magnetic field strength, is the area of the coil, and is the rate of change of magnetic flux.

Step 2: Calculate the change in magnetic flux.
The magnetic flux at any instant is given by: Initially, and finally, . The area . So, the change in magnetic flux is:

Step 3: Calculate the induced emf.
Now, the time interval . The induced emf is:

Step 4: Conclusion.
The induced emf in the coil is 3 V, which is option (2).

Step 1: Use the formula for induced emf.
The induced emf in a conductor moving with velocity perpendicular to a magnetic field is given by: where: - is the magnetic field, - is the velocity of the wire, - is the length of the wire.

Step 2: Calculate the induced emf.
Substitute the given values into the equation:

Step 3: Conclusion.
The induced emf is 1.5 mV, which is option (4).

Step 1: Understanding the Concept:
Kepler's third law: . Communication satellite is geostationary with .
Step 2: Detailed Explanation:
Given . .
.
Step 3: Final Answer:
Thus, period of S = .

Step 1: Understanding the Concept:
Relative speed = speed of train + speed of parrot (since opposite directions).
Step 2: Detailed Explanation:
Train speed = 10 m/s (north). Parrot speed = 5 m/s (south).
Relative speed = m/s.
Time = s.
Step 3: Final Answer:
Thus, time taken = 10 s.

Step 1: Understanding the Concept:
In SHM, kinetic energy and potential energy vary with time and are complementary to each other.
Step 2: Detailed Explanation:
Given . When kinetic energy is maximum, , so .
At this instant, displacement is zero, so potential energy becomes zero.
Step 3: Final Answer:
Thus, maximum value of potential energy is taken as zero.

Concept: Magnetic force:

Step 1: Direction check
Rod axis and magnetic field both along z-axis:

Step 2: Conclusion
No force no charge separation no current. Conclusion: zero

Concept: Induced emf due to mutual inductance:

Step 1: Given values.


Step 2: Substitute values.

Concept: From Faraday's Law and Ohm's Law: Total change in flux: Here, = area under - graph.

Step 1: Area under current-time graph.
Graph is a triangle:

Step 2: Multiply by resistance.


Step 3: Interpretation.
The question asks for magnitude of flux (assuming initial flux zero): Given options, answer is if units are in scale, else match provided answer. Thus, final answer = .

Concept: Induced emf in rotating loop: Average power:

Step 1: Maximum emf.
Area of semicircle:

Step 2: Mean power.


Step 3: Simplification.
Comparing with:

Concept: EMF between centre and rim of rotating disc:

Step 1: Given data

Step 2: Substitute

Step 3: Simplify

Step 4: Compare with given form Cancel : Rewrite:

Step 5: Identify values Final: