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A conducting circular loop made of a thin wire, has area 3.5 × 10 –3m2 and resistance 10W. It is placed perpendicular to a time dependent magnetic field B (t) = (0.4T) sin (50pt). The net charge flowing through the loop during t = 0 s and t = 10 ms is close to:
- a)1.4 × 10–4 mC
- b)7.0 × 10–4 mC
- c)21 × 10–4 mC
- d)6 × 10–4 mC
Correct answer is option 'A'. Can you explain this answer?
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A conducting circular loop made of a thin wire, has area 3.5 × 10 –3m...
Net charge
= 1.4 × 10– 4 mC
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A conducting circular loop made of a thin wire, has area 3.5 × 10 –3m...
Given information:
- Area of the circular loop: 3.5 × 10^(-3) m^2
- Resistance of the loop: 10 Ω
- Time-dependent magnetic field: B(t) = (0.4 T) sin(50πt)
- Time interval: t = 0 s to t = 10 ms
To find:
The net charge flowing through the loop during the given time interval.
Formula:
The emf induced in a conducting loop is given by Faraday's Law of Electromagnetic Induction:
ε = -dΦ/dt
Where ε is the induced emf and Φ is the magnetic flux through the loop.
The magnetic flux through the loop is given by the formula:
Φ = B(t) * A
Where B(t) is the magnetic field at time t and A is the area of the loop.
The current flowing through the loop is given by Ohm's Law:
I = V/R
Where I is the current, V is the induced emf, and R is the resistance of the loop.
The charge flowing through the loop is given by:
Q = I * t
Where Q is the charge, I is the current, and t is the time interval.
Solution:
1. Calculate the magnetic flux at t = 0 s:
Φ_1 = B(0) * A
= (0.4 T) * sin(50π * 0) * 3.5 × 10^(-3) m^2
= 0
2. Calculate the magnetic flux at t = 10 ms:
Φ_2 = B(10 ms) * A
= (0.4 T) * sin(50π * (10 × 10^(-3))) * 3.5 × 10^(-3) m^2
3. Calculate the change in magnetic flux:
ΔΦ = Φ_2 - Φ_1
4. Calculate the induced emf:
ε = -dΦ/dt
= -ΔΦ / (10 ms - 0 s)
5. Calculate the current:
I = ε / R
6. Calculate the charge:
Q = I * t
= (ε / R) * (10 ms - 0 s)
Final answer:
The net charge flowing through the loop during t = 0 s and t = 10 ms is approximately 1.4 × 10^(-4) mC. Therefore, the correct answer is option A.
- Area of the circular loop: 3.5 × 10^(-3) m^2
- Resistance of the loop: 10 Ω
- Time-dependent magnetic field: B(t) = (0.4 T) sin(50πt)
- Time interval: t = 0 s to t = 10 ms
To find:
The net charge flowing through the loop during the given time interval.
Formula:
The emf induced in a conducting loop is given by Faraday's Law of Electromagnetic Induction:
ε = -dΦ/dt
Where ε is the induced emf and Φ is the magnetic flux through the loop.
The magnetic flux through the loop is given by the formula:
Φ = B(t) * A
Where B(t) is the magnetic field at time t and A is the area of the loop.
The current flowing through the loop is given by Ohm's Law:
I = V/R
Where I is the current, V is the induced emf, and R is the resistance of the loop.
The charge flowing through the loop is given by:
Q = I * t
Where Q is the charge, I is the current, and t is the time interval.
Solution:
1. Calculate the magnetic flux at t = 0 s:
Φ_1 = B(0) * A
= (0.4 T) * sin(50π * 0) * 3.5 × 10^(-3) m^2
= 0
2. Calculate the magnetic flux at t = 10 ms:
Φ_2 = B(10 ms) * A
= (0.4 T) * sin(50π * (10 × 10^(-3))) * 3.5 × 10^(-3) m^2
3. Calculate the change in magnetic flux:
ΔΦ = Φ_2 - Φ_1
4. Calculate the induced emf:
ε = -dΦ/dt
= -ΔΦ / (10 ms - 0 s)
5. Calculate the current:
I = ε / R
6. Calculate the charge:
Q = I * t
= (ε / R) * (10 ms - 0 s)
Final answer:
The net charge flowing through the loop during t = 0 s and t = 10 ms is approximately 1.4 × 10^(-4) mC. Therefore, the correct answer is option A.
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A conducting circular loop made of a thin wire, has area 3.5 × 10 –3m2 and resistance 10W. It is placed perpendicular to a time dependent magnetic field B (t) = (0.4T) sin (50pt). The net charge flowing through the loop during t = 0 s and t = 10 ms is close to:a)1.4 × 10–4 mCb)7.0 × 10–4 mCc)21 × 10–4 mCd)6 × 10–4 mCCorrect answer is option 'A'. Can you explain this answer?
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A conducting circular loop made of a thin wire, has area 3.5 × 10 –3m2 and resistance 10W. It is placed perpendicular to a time dependent magnetic field B (t) = (0.4T) sin (50pt). The net charge flowing through the loop during t = 0 s and t = 10 ms is close to:a)1.4 × 10–4 mCb)7.0 × 10–4 mCc)21 × 10–4 mCd)6 × 10–4 mCCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A conducting circular loop made of a thin wire, has area 3.5 × 10 –3m2 and resistance 10W. It is placed perpendicular to a time dependent magnetic field B (t) = (0.4T) sin (50pt). The net charge flowing through the loop during t = 0 s and t = 10 ms is close to:a)1.4 × 10–4 mCb)7.0 × 10–4 mCc)21 × 10–4 mCd)6 × 10–4 mCCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting circular loop made of a thin wire, has area 3.5 × 10 –3m2 and resistance 10W. It is placed perpendicular to a time dependent magnetic field B (t) = (0.4T) sin (50pt). The net charge flowing through the loop during t = 0 s and t = 10 ms is close to:a)1.4 × 10–4 mCb)7.0 × 10–4 mCc)21 × 10–4 mCd)6 × 10–4 mCCorrect answer is option 'A'. Can you explain this answer?.
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