VARDAAN LEARNING INSTITUTE

1. Yes. Changing current in coil A produces a changing magnetic field. This changing field passes through coil B, inducing a current in it (Electromagnetic Induction).
2. Force $F = qvB\sin\theta$. Force will be zero if $\sin\theta = 0$, i.e., the alpha particle moves parallel ($\theta=0^\circ$) or anti-parallel ($\theta=180^\circ$) to the magnetic field.
3. Field is Up. Velocity is North. Using Fleming's Left Hand Rule: Forefinger (Up), Middle (North) -> Thumb points West. So, the proton deflects towards West. The path will be curved (Wait... circular arc, then helical if not uniform? Here, simply it deflects towards West).
4. Inside the core of the solenoid, the field is NOT zero; it is uniform and strong. However, if you mean inside the copper wire itself, or outside the ideal solenoid sideways, it is negligible. (Corrected Concept: In a hollow solenoid, the field is uniform inside the empty space. It is zero OUTSIDE the solenoid, not inside). *Actually, the question asked "Why is field inside hollow solenoid zero?" which is a trick question or misconception. The answer should correct it: Field is uniform inside, not zero. If it refers to neutral points, usually they are outside.*
5. Yes, work done is zero. The magnetic force acts perpendicular to the velocity ($F \perp v$). Work $W = \int F \cdot dl$ $= \int F \cdot v dt$. Since $F \cdot v = 0$ (dot product is zero for perpendicular vectors), Work is zero. Kinetic energy remains constant.
6. Stable equilibrium occurs when the magnetic dipole moment (normal to the loop) is parallel to the magnetic field ($\theta=0^\circ$). The potential energy is minimum (-MB).
7. The resistance of a fuse wire is higher than that of the mains connecting wire. This ensures that more heat is generated in the fuse ($H \propto R$) so it melts first.
8. They repel. Field lines between them are in the same direction, creating a region of stronger field/pressure that pushes them apart. (Or use Fleming's Rule on one wire from field of other).
9. Zero. If the conductor is parallel to the field, Force is zero ($F=BIl\sin(0)=0$). If force is zero, torque is zero (for straight wire translational context).
10. Gauss's law for magnetism is $\oint B \cdot dA = 0$ (Net flux is zero because monopoles don't exist). If monopoles existed, this integral would equal $\mu_0 q_m$ (magnetic charge enclosed), similar to Gauss's law for electrostatics.
11. Radius $r = mv/qB$. If speed $v$ is doubled, the radius $r$ will also be doubled.
12. No. Transformer works on the principle of mutual induction which requires a changing magnetic flux. DC produces a constant magnetic field, so no flux change, no induction.
13. Electromagnets are temporary and can be made very strong by increasing current/turns. They also allow turning the motor on/off and controlling speed, which permanent magnets don't allow easily.
14. Connecting 220V appliance to 440V will cause double voltage -> double current (initially) -> Power $P=V^2/R$ becomes 4 times. The massive current will immediately blow the fuse (if rated correctly for 220V) protecting the appliance. If no fuse, the appliance burns.
15. The circuit breaks, so no current flows. Appliances stop working. However, the Live wire is still connected, so the internal components are at 220V potential (Shock hazard if touched).

Case I

16. Magnetic Resonance Imaging.
17. Heart and Brain.
18. By the movement of ions (charged particles) along the nerve cells.
19. The earth's magnetic field is much weaker than the MRI magnetic field (which is about 1 Tesla, approx 20,000 times earth's field).
20. Tesla (T).

Case II

21. Tin-Lead alloy (Solder). Chosen because it has a low melting point.
22. Power $P=2000W, V=220V$. Current $I = 2000/220$ $\approx 9.09A$. Since $9.09A > 5A$ rating, the fuse will blow. No, it cannot be used.
23. The rated current determining the heat generated ($H \propto I^2$). Thicker wire has less resistance and carries more current.
24. Live Wire.
25. To generate enough heat to melt quickly ($H = I^2Rt$). If resistance is too low, it might not heat up enough to melt before damage occurs elsewhere.

Case III

26. Whenever the magnetic flux linked with a closed coil changes, an induced electromotive force (emf) and current is produced in it.
27. No. There is no relative motion, so no change in magnetic flux.
28. Fleming's Right Hand Rule.
29. AC (Alternating Current). As the coil rotates, the direction of induced current reverses every half rotation.
30. Mechanical Energy to Electrical Energy.

31. (b) Both True but R is NOT correct explanation. R explains Uniformity, not Bar Magnet behavior (which is due to field coming out at ends).
32. (d) A is False but R is True. Field *decreases* as we move away ($B \propto 1/r$).
33. (a) Both True and R is correct explanation.
34. (a) Both True and R is correct explanation.
35. (a) Both True and R is correct explanation. ($F=qvB$, if $v=0, F=0$).
36. (d) A is False (AC generator uses Slip Rings, DC Motor uses Split Rings). R is True (Split rings reverse current).
37. (a) Both True and R is correct explanation.
38. (a) Both True and R is correct explanation. (Technically R describes the path, confirming it is closed).
39. (a) Both True and R is correct explanation.
40. (d) A is False. A wire carrying DC *does* produce a magnetic field and deflects a compass (Oersted's Experiment). R is True.
41. (a) Both True and R is correct explanation.
42. (a) Both True and R is correct explanation.
43. (a) Both True and R is correct explanation.
44. (d) A is False. 60W bulb glows brighter in series because it has higher resistance and $P=I^2R$. (Correct logic).
45. (d) A is False (Left is for Force). R is False (Right is for Current). Both are false. Wait, standard options only allow (d) A False R True usually, but here both are indeed False. *Correction: Left Hand = Force. Right Hand = Current. So Reason is also False. Option (e) Both False? Or typo in assertion logic. Let's assume standard Class 10 logic: A is False. R is False.* Wait, let me check the question text again. Assertion: Left Hand Rule -> Induced Current (False). Reason: Right Hand Rule -> Force (False). Answer: Both statements are False. (If forced to choose from a-d standard, it's invalid. I will write "Both are False").