Magnetic Effects of Electric Current — Important Questions

Answers

• If $\theta ={90}^{\circ }$, the force is maximum and perpendicular to both $v$ and $B$. The electron will move in a circular path.
• If $\theta =0^{\circ }$ or $\theta ={180}^{\circ }$, the force is zero, and the electron will continue to move in a straight line without any change in its velocity.
• For any other angle $\theta$ ($0^{\circ }<\theta <{180}^{\circ }$), the electron will move in a helical path.
  8. (a) The diagram shows a conductor AB carrying current from A to B, placed in a magnetic field directed downwards. Applying Fleming's left-hand rule (forefinger for magnetic field downwards, middle finger for current from A to B), the thumb points towards the right. Therefore, the force on the conductor will be directed towards the right.
  (b) If the direction of current through it is reversed (from B to A), then applying Fleming’s left-hand rule, the force will be directed towards the left.
  9. (c) velocity.
  Justification: When a charged particle moves in a magnetic field, it experiences a force perpendicular to its velocity. This force changes the direction of the velocity but not its magnitude (speed). Since velocity is a vector quantity (having both magnitude and direction), a change in direction means a change in velocity. Mass is an intrinsic property and remains constant. Momentum is the product of mass and velocity ($p=mv$). Since the velocity changes, the momentum also changes. However, the question asks which property can change. While momentum also changes, velocity is the most direct answer reflecting the change in motion. If the magnetic field is uniform and the particle enters perpendicular to it, the speed remains constant, but the velocity changes continuously.
  10. Case Study:
  (a) The magnetic field lines around a current-carrying circular loop are concentric circles near the wire, which become larger arcs as they move away. At the center of the loop, these arcs appear as straight lines. The field lines form closed loops, emerging from one face of the loop (acting as a north pole) and entering the other face (acting as a south pole).
  (b) If the number of turns in the coil is increased, the magnetic field strength at the center of the loop increases. This is because the field due to each turn adds up.
  (c) The rule used to determine the direction of the magnetic field within the loop is the Right-Hand Thumb Rule.
  11. Data Interpretation:
  (a) The deflection of the compass needle indicates the presence and direction of the magnetic field produced by the current-carrying wire.
  (b) Based on the data, as the distance from the wire increases (from 1 cm to 4 cm), the deflection of the compass needle decreases (from 45 degrees to 10 degrees). This shows that the magnetic field strength decreases as the distance from the wire increases.
  (c) If the current in the wire is increased, the magnetic field strength will increase, leading to a larger deflection of the compass needle.
  12. Situational:
  (a) The three types of wires are:
• Live wire: Red insulation
• Neutral wire: Black insulation
• Earth wire: Green insulation
  (b) The earth wire is connected to the metallic body of appliances. Its function is to provide a low-resistance path for current to flow to the earth in case of any leakage of current to the metallic body. This prevents the user from getting a severe electric shock.
  (c) The potential difference between the live wire and the neutral wire in India is 220 V.
  13. Application:
  (a) Power ($P$) = 2 kW = 2000 W. Voltage ($V$) = 220 V.
  We know that $P=V\times I$.
  Therefore, Current ($I$) = $P\mathrm{/}V$ = 2000 W / 220 V = 9.09 A (approximately).
  (b) The current drawn by the heater is approximately 9.09 A. The fuse is rated for 5 A. Since the current drawn by the heater (9.09 A) is greater than the fuse rating (5 A), the fuse wire will melt and blow, disconnecting the circuit. Thus, the heater will not operate, and the fuse will blow.
  14. Fleming’s Left-Hand Rule: If you stretch the thumb, forefinger, and middle finger of your left hand so that they are mutually perpendicular to each other, and if the forefinger points in the direction of the magnetic field and the middle finger points in the direction of the current, then the thumb will point in the direction of the force acting on the current-carrying conductor.
  Use: This rule is used to determine the direction of the force experienced by a current-carrying conductor when it is placed in an external magnetic field.
  15. Two magnetic field lines cannot intersect each other because if they did, it would mean that at the point of intersection, the compass needle would point in two different directions simultaneously, which is impossible. A compass needle can only point in one direction at any given point.
  16. Diagram:
  (Imagine a diagram showing a vertical straight conductor with an arrow pointing upwards indicating the direction of current. Concentric circles are drawn around the conductor, with arrows showing a counter-clockwise direction for the magnetic field lines when viewed from above, consistent with the Right-Hand Thumb Rule.)
  17. Short-circuiting: A short circuit occurs when the live wire and the neutral wire come into direct contact, often due to damaged insulation or a fault in an appliance. This creates a path of very low resistance, causing a very large current to flow through the circuit.
  Function of Fuse: An electric fuse is a safety device containing a wire of a low melting point. When an abnormally large current flows due to a short circuit (or overloading), the fuse wire heats up due to Joule heating, melts, and breaks the circuit. This stops the flow of unduly high current, preventing damage to the appliances and the wiring.
  18. Assertion-Reason:
  (A) Both assertion and reason are true, and reason is the correct explanation of assertion.
  Explanation: The magnetic field lines inside a long solenoid are parallel straight lines, which means the field is uniform at all points within the solenoid. This uniformity is a direct consequence of the arrangement of field lines as parallel straight lines.
  19. (C) A solenoid
  20. The magnitude of the force experienced by a current-carrying conductor placed in a magnetic field is given by $F=IlB\sin \theta$, where $I$ is the current, $l$ is the length of the conductor, $B$ is the magnetic field strength, and $\theta$ is the angle between the conductor and the magnetic field.
  When $\theta ={90}^{\circ }$, $\sin {90}^{\circ }=1$, so the force is maximum: $F_{max}=IlB$.
  When $\theta ={30}^{\circ }$, $\sin {30}^{\circ }=\frac{1}{2}$. The force will be $F=IlB\times \frac{1}{2}=\frac{1}{2}{F}_{max}$.
  Therefore, if the angle changes from ${90}^{\circ }$ to ${30}^{\circ }$, the magnitude of the force will reduce to half of its maximum value.