A 1000-turn coil of effective area $0.06\ m^2$ is kept perpendicular to a magnetic field $4 \times 10^{-5}\ T$. When the plane of the coil is rotated by $90^0$ around any of its coplanar axes in 0.2 s, the emf induced in the coil will be:

## CORE INFORMATION\n✓ **Answer**: B. 12 mV\n## CONCEPT FRAMEWORK\n **Primary Concept**: Faraday's Law of Electromagnetic Induction\n **Related Topics**: Magnetic flux, induced emf, rotational motion\n **Prerequisites**: Understanding of magnetic fields, area vectors, and calculus (for a more rigorous derivation).\n## SOLUTION PATHWAY\n**Given Information**:\n N = 1000 turns\n A = 0.06 m²\n B = 4 × 10⁻⁵ T\n θ = 90°\n Δt = 0.2 s\n Initial angle = 0°\n Final angle = 90°\n**Method & Steps**:\n 1. Calculate the change in magnetic flux (ΔΦ):\n Reasoning: The magnetic flux is given by Φ = NBAcosθ, where θ is the angle between the magnetic field and the area vector. The change in flux is the difference between the final and initial flux.\n Formula/Rule: ΔΦ = NBA(cosθ₂ - cosθ₁)\n Working: ΔΦ = 1000 × (4 × 10⁻⁵ T) × (0.06 m²) × (cos90° - cos0°) = -0.0024 Wb\n 2. Apply Faraday's Law to find the induced emf:\n Reasoning: Faraday's Law states that the induced emf is equal to the negative rate of change of magnetic flux.\n Formula/Rule: ε = -ΔΦ/Δt\n Working: ε = -(-0.0024 Wb) / 0.2 s = 0.012 V = 12 mV\n 3. State the final answer:\n Result: 12 mV\n Verification: The units are correct (Volts or mV). The magnitude is reasonable given the parameters.\n ## OPTION ANALYSIS\nA :x: Incorrect calculation of magnetic flux or application of Faraday's law.\nB ✓: Correct application of Faraday's Law and calculation of induced emf.\nC :x: Incorrect calculation likely due to an error in handling the cosine function or units.\nD :x: Significant error in calculation, possibly misinterpreting the given parameters.\n ## LEARNING AIDS\n **Common Mistakes**:\n 1.Ignoring the negative sign in Faraday's Law: This only affects the direction of the induced current, but the magnitude remains unchanged.\n 2.Incorrectly calculating the change in magnetic flux: Ensure proper use of the cosine function and unit conversions.\n **Quick Tips**:\n 1.Remember the formula: ε = -N(ΔΦ/Δt) = -NBA(cosθ₂ - cosθ₁)/Δt\n 2.Draw a diagram to visualize the orientation of the coil and magnetic field.

A rectangular coil of 800 turns with dimensions $0.1\ m \times 0.05\ m$ is placed in a uniform magnetic field of $5 \times 10^{-5}\ T$. If the coil is rotated by $90^0$ in 0.1 s about an axis perpendicular to the field, what is the induced emf?

## CORE INFORMATION\n✓ **Answer**: B. 2 mV\n## CONCEPT FRAMEWORK\n **Primary Concept**: Faraday's Law of Electromagnetic Induction\n **Related Topics**: Magnetic flux, induced emf, rotational motion\n **Prerequisites**: Understanding of magnetic fields, area calculation, and basic algebra.\n## SOLUTION PATHWAY\n**Given Information**:\n N = 800 turns\n A = 0.1 m × 0.05 m = 0.005 m²\n B = 5 × 10⁻⁵ T\n θ = 90°\n Δt = 0.1 s\n Initial angle = 0°\n Final angle = 90°\n**Method & Steps**:\n 1. Calculate the change in magnetic flux (ΔΦ):\n Reasoning: Similar to question 1, we use the formula for magnetic flux and find the change in flux when the coil rotates 90 degrees.\n Formula/Rule: ΔΦ = NBA(cosθ₂ - cosθ₁)\n Working: ΔΦ = 800 × (5 × 10⁻⁵ T) × (0.005 m²) × (cos90° - cos0°) = -0.0002 Wb\n 2. Apply Faraday's Law to find the induced emf:\n Reasoning: The induced emf is the rate of change of magnetic flux.\n Formula/Rule: ε = -ΔΦ/Δt\n Working: ε = -(-0.0002 Wb) / 0.1 s = 0.002 V = 2 mV\n 3. State the final answer:\n Result: 2 mV\n Verification: Units are correct, and the magnitude is reasonable for the given parameters.\n ## OPTION ANALYSIS\nA :x: Incorrect calculation, possibly a mistake in area calculation or Faraday's Law application.\nB ✓: Correct calculation of induced emf using Faraday's Law.\nC :x: Error in calculation, potentially a mistake in handling the numbers or units.\nD :x: Significant error, likely due to a misunderstanding of the problem or a major calculation mistake.\n ## LEARNING AIDS\n **Common Mistakes**:\n 1.Forgetting to account for the number of turns (N) in the coil.\n 2.Incorrectly calculating the area of the rectangular coil.\n **Quick Tips**:\n 1.Always write down the given information and the formula before starting the calculation.\n 2.Double-check your calculations to avoid simple arithmetic errors.

A square coil of 500 turns with side 10 cm is placed perpendicular to a magnetic field of $2 \times 10^{-4}\ T$. If the coil is rotated through $90^0$ in 0.05 s about an axis in its plane, what is the magnitude of the average induced emf?

## CORE INFORMATION\n✓ **Answer**: B. 20 mV\n## CONCEPT FRAMEWORK\n **Primary Concept**: Faraday's Law of Electromagnetic Induction\n **Related Topics**: Magnetic flux, induced emf, rotational motion\n **Prerequisites**: Understanding of magnetic fields, area calculation for a square, and Faraday's Law.\n## SOLUTION PATHWAY\n**Given Information**:\n N = 500 turns\n side = 10 cm = 0.1 m\n A = (0.1 m)² = 0.01 m²\n B = 2 × 10⁻⁴ T\n θ = 90°\n Δt = 0.05 s\n Initial angle = 0°\n Final angle = 90°\n**Method & Steps**:\n 1. Calculate the change in magnetic flux (ΔΦ):\n Reasoning: The change in flux is calculated using the formula for magnetic flux and the angle change.\n Formula/Rule: ΔΦ = NBA(cosθ₂ - cosθ₁)\n Working: ΔΦ = 500 × (2 × 10⁻⁴ T) × (0.01 m²) × (cos90° - cos0°) = -0.001 Wb\n 2. Apply Faraday's Law to find the induced emf:\n Reasoning: Faraday's Law gives the induced emf as the rate of change of magnetic flux.\n Formula/Rule: ε = -ΔΦ/Δt\n Working: ε = -(-0.001 Wb) / 0.05 s = 0.02 V = 20 mV\n 3. State the final answer:\n Result: 20 mV\n Verification: The units are correct (Volts or mV). The magnitude is plausible considering the given values.\n ## OPTION ANALYSIS\nA :x: Error in calculation, likely a mistake in the area calculation or application of Faraday's Law.\nB ✓: Correct application of Faraday's Law and accurate calculation of induced emf.\nC :x: Incorrect calculation, possibly due to an error in handling the numbers or units.\nD :x: Significant error, likely from a misunderstanding of the problem or a major calculation mistake.\n ## LEARNING AIDS\n **Common Mistakes**:\n 1.Forgetting to convert centimeters to meters when calculating the area.\n 2.Misinterpreting the angle of rotation and its effect on the magnetic flux.\n **Quick Tips**:\n 1.Always ensure consistent units throughout the calculation.\n 2.Draw a diagram to visualize the coil's orientation and the magnetic field.

A coil of 1200 turns and area $0.04\ m^2$ is rotated through $90^0$ in a magnetic field of $6 \times 10^{-5}\ T$ in 0.15 seconds. Calculate the magnitude of the average emf induced in the coil.

## CORE INFORMATION\n✓ **Answer**: B. 19.2 mV\n## CONCEPT FRAMEWORK\n **Primary Concept**: Faraday's Law of Electromagnetic Induction\n **Related Topics**: Magnetic flux, induced emf, rotational motion\n **Prerequisites**: Understanding of magnetic fields, Faraday's Law, and basic algebra.\n## SOLUTION PATHWAY\n**Given Information**:\n N = 1200 turns\n A = 0.04 m²\n B = 6 × 10⁻⁵ T\n θ = 90°\n Δt = 0.15 s\n Initial angle = 0°\n Final angle = 90°\n**Method & Steps**:\n 1. Calculate the change in magnetic flux (ΔΦ):\n Reasoning: We find the change in flux as the coil rotates 90 degrees in the magnetic field.\n Formula/Rule: ΔΦ = NBA(cosθ₂ - cosθ₁)\n Working: ΔΦ = 1200 × (6 × 10⁻⁵ T) × (0.04 m²) × (cos90° - cos0°) = -0.00288 Wb\n 2. Apply Faraday's Law to find the induced emf:\n Reasoning: Faraday's Law relates the induced emf to the rate of change of magnetic flux.\n Formula/Rule: ε = -ΔΦ/Δt\n Working: ε = -(-0.00288 Wb) / 0.15 s = 0.0192 V = 19.2 mV\n 3. State the final answer:\n Result: 19.2 mV\n Verification: Units are correct. The magnitude is reasonable given the parameters.\n ## OPTION ANALYSIS\nA :x: Error in calculation, possibly an arithmetic error or mistake in applying Faraday's Law.\nB ✓: Correct calculation of the induced emf using Faraday's Law.\nC :x: Incorrect calculation, potentially a mistake in handling numbers or units.\nD :x: Significant error, likely due to a misunderstanding of the problem or a major calculation mistake.\n ## LEARNING AIDS\n **Common Mistakes**:\n 1.Making errors in the calculation of the change in magnetic flux.\n 2.Forgetting to include the number of turns (N) in the Faraday's Law equation.\n **Quick Tips**:\n 1.Always double-check your calculations to avoid simple arithmetic errors.\n 2.Pay close attention to units and ensure consistency throughout the calculation.

The correct Option is "19.2 mV"

NEET Physics Electromagnetic Induction Magnetic Flux & Faraday'S Law & Lenz'S Law MCQs

📑 Chapter:Electromagnetic Induction

🎯Topic:Magnetic Flux & Faraday'S Law & Lenz'S Law

PYQ Year :2017

🎓 Ncert Level:Application

🎯Difficulty :Medium

⚡ Time Required :5 mins

🔄Ncert Concepts :Electromagnetic Induction, Solenoid, Magnetic Flux

10.

A coil of 75 turns and radius 0.012 m is placed at the center of a long solenoid with diameter 0.14 m and 18000 turns per meter, their axes aligned. The current in the solenoid decreases uniformly from 6 A to 0 A in 0.06 s. With a coil resistance of $9\pi^2\,\Omega$ , find the total charge flowing through the coil.