Magnetic Effects Of Current And Magnetism

Step 1: Concept
Magnetic moment .
Step 2: Analysis
Current . Area .
Step 3: Conclusion
.
Final Answer: (A)

Step 1: Concept
According to Curie's Law, (where is in Kelvin).
Step 2: Analysis
. . .
Step 3: Conclusion
.
Final Answer: (B)

Step 1: Setup
The sequences with an even number of 0's can have 0, 2, 4, ... zeros.
Step 2: Binomial Sum
The total number of ways =
Step 3: Identity
It is a standard binomial identity that the sum of even-indexed coefficients equals .
Final Answer: (a)

Step 1: Nature of Nitro Group
The nitro group ( ) is a strong electron-withdrawing group due to resonance and inductive effects.
Step 2: Impact on Ring
It withdraws electrons specifically from the ortho and para positions. This significantly decreases electron density at those sites.
Step 3: Directing Effect
As a result, the meta position has a relatively higher electron density compared to ortho and para, making it the preferred site for electrophilic attack.
Final Answer: (a)

Step 1: Understanding thermo emf.
Thermo emf is the voltage generated across the junctions of two dissimilar conductors due to the difference in temperature, as described by the Seebeck effect.

Step 2: Analyzing the relationship between temperature and thermo emf.
- In most materials, as the temperature of the hot junction increases, the thermo emf decreases. This happens because the material properties that contribute to the thermo emf often become less effective at higher temperatures.

Step 3: Conclusion.
Therefore, the correct answer is (2) because the thermo emf typically decreases as the temperature increases.

Step 1: Understanding the motion of charged particles in a magnetic field.
When charged particles such as protons and -particles enter a magnetic field perpendicular to their motion, they undergo circular motion. The periodic time (T) for a charged particle moving in a magnetic field is given by the formula: where is the mass of the particle, is the charge, and is the magnetic field strength.

Step 2: Comparing proton and -particle.
- A proton has a charge and mass . An -particle has a charge and mass . - Since the -particle has twice the charge and four times the mass of the proton, its periodic time will be longer than that of the proton.
- The periodic time for the proton is given as 25 s for 5 revolutions, which means the periodic time is 5 s. The periodic time for the -particle would be:

Step 3: Conclusion.
The periodic time for the -particle is 10 s. Thus, the correct answer is (3).

Step 1: Understanding the function of a voltmeter and ammeter.
- A voltmeter measures the potential difference between two points in a circuit. It is always connected in parallel with the component across which the voltage is to be measured. Therefore, it must have high resistance to prevent it from drawing excessive current.
- An ammeter measures the current passing through a component. It must be connected in series with the component, and it must have very low resistance to avoid altering the current.

Step 2: Identifying the incorrect statement.
- Statement (1) is correct: A voltmeter must have high resistance.
- Statement (2) is correct: An ammeter should have low resistance.
- Statement (3) is incorrect: An ammeter is always placed in series with the conductor, not in parallel.
- Statement (4) is correct: A voltmeter is placed in parallel across the conductor.

Step 3: Conclusion.
The wrong statement is (3), as the ammeter should be placed in series with the conductor.

Step 1: Use the formula for shunt resistance.
The shunt resistance is given by: where is the resistance of the galvanometer and is the factor by which the current is divided.

Step 2: Calculate the shunt resistance.
Here, 10 percent of the current passes through the galvanometer, so . Substituting the values:

Step 3: Conclusion.
The shunt resistance is 11 ohm, which is option (2).

Step 1: Understanding the Concept:
1 dyne = N, 1 cm = m.
Step 2: Detailed Explanation:
.
Step 3: Final Answer:
Thus, .

Step 1: Understanding the Concept:
Use ideal gas equation .
Step 2: Detailed Explanation:
Given: , , , , .
.
Step 3: Final Answer:
Thus, .

Step 1: Understanding the Concept:
For SHM, displacement . Velocity . Maximum velocity .
Step 2: Detailed Explanation:
Given masses are equal and velocities are equal. In SHM, when velocity is maximum, . Since velocity is same for all three bodies, .
Step 3: Final Answer:
Thus, .

Step 1: Understanding the Concept:
Induced emf . It depends on the rate of change of current.
Step 2: Detailed Explanation:
When the switch is pressed, current increases and induces emf opposing the rise.
When the switch is opened, current decreases and induces emf opposing the fall.
In both cases, the induced emf acts to oppose the change in current, and is considered equal in magnitude under ideal conditions.
Step 3: Final Answer:
Thus, .

Step 1: For single turn, . For n turns, radius becomes .

Step 2: .

Step 1: For a circular loop, .

Step 2: When bent into double loop, each loop has radius . Field due to each: . Two loops: .

Step 1: turns/cm turns/m. T.

Step 1: , where M is net magnetic moment.

Step 2: Similar poles same side: . Opposite poles: .

Step 3: , so , so .

Step 1: , so . .

Step 1: Understanding the Concept:
For a long solenoid, , where is the number of turns per unit length.
Step 2: Detailed Explanation:
. This is independent of the diameter .
Step 3: Final Answer:
The magnetic field is independent of .

Step 1: Understanding the Concept:
Magnetic field due to a long straight wire: .
Step 2: Detailed Explanation:
At the midpoint, distance from each wire is . Magnetic fields due to each wire are equal in magnitude but opposite in direction (by right-hand rule). Hence, net magnetic field is zero.
Step 3: Final Answer:
The magnetic field is zero.

Step 1: Understanding the Concept:
Force between two parallel conductors: .
Step 2: Detailed Explanation:
(attractive, since currents in same direction). (repulsive, since currents in opposite direction). So but opposite in direction, hence .
Step 3: Final Answer:
.

Step 1: Understanding the Concept:
For tangent galvanometer, .
Step 2: Detailed Explanation:
A, . . So , hence A. Then .
Step 3: Final Answer:
The resistance to be connected is .

Step 1: Understanding the Concept:
Magnetic field due to a long straight wire is . Force on a moving charge is .
Step 2: Detailed Explanation:
T.
N.
Step 3: Final Answer:
The force is N.

Step 1: Understanding the Concept:
The magnetic field at the centre of a long solenoid is , where is the number of turns per unit length.
Step 2: Detailed Explanation:
turns/m.
So, T.
Step 3: Final Answer:
The magnetic field is T.

Step 1: Understanding the Concept:
For a charged particle to move undeflected in a straight line, the net force on it must be zero.
Step 2: Detailed Explanation:
The Lorentz force is . For no deflection, , so . This implies and is perpendicular to both and . Since is along the line of motion, and are perpendicular to each other.
Step 3: Final Answer:
Thus and the two fields are perpendicular.

Step 1: Understanding the Concept:
Radius .
Step 2: Detailed Explanation:

For He :
For O :
So same deflection.
Step 3: Final Answer:
All ions are deflected equally.

Concept:

Step 1: Rearrange.


Step 2: Substitute.