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A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is
- a)4.8 π μV
- b)0.8 π μV
- c)1.6 π μV
- d)3.2 π μV
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A conducting circular loop is placed in a uniform magnetic field of 0....
Induced emf in th e loop is gi ven by
e = -B. dA/dt where A is the area of the loop.
r = 2cm = 2 × 10–2 m
dr = 2 mm = 2 × 10–3 m
dt = 1s
= 0.32 π × 10–5V
= 3.2 π ×10–6V
= 3.2 π μV
e = -B. dA/dt where A is the area of the loop.
r = 2cm = 2 × 10–2 m
dr = 2 mm = 2 × 10–3 m
dt = 1s
= 0.32 π × 10–5V
= 3.2 π ×10–6V
= 3.2 π μV
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A conducting circular loop is placed in a uniform magnetic field of 0....
To find the induced emf in the loop, we can use Faraday's law of electromagnetic induction:
emf = -dφ/dt
where emf is the induced electromotive force, dφ is the change in magnetic flux, and dt is the change in time.
The magnetic flux through the loop is given by:
Φ = B⋅A
where B is the magnetic field strength and A is the area of the loop.
Since the loop is circular and its plane is perpendicular to the magnetic field, the area of the loop remains constant as the radius shrinks.
Therefore, the change in magnetic flux is simply the product of the change in magnetic field and the constant area:
dΦ/dt = B⋅dA/dt
Since dA/dt is the rate at which the area changes with time, and the radius is shrinking at 2 mm/s, we have:
dA/dt = -2πr(dr/dt)
where r is the radius of the loop.
Substituting this expression into the equation for the change in magnetic flux, we get:
dΦ/dt = -2πr(dr/dt)B
Now we can substitute this expression into Faraday's law of electromagnetic induction to find the induced emf:
emf = -dΦ/dt
= -(-2πr(dr/dt)B)
= 2πr(dr/dt)B
Substituting the given values of r = 2 cm = 0.02 m, dr/dt = -2 mm/s = -0.002 m/s, and B = 0.04 T, we can calculate the induced emf:
emf = 2π(0.02)(-0.002)(0.04)
= -0.00008π V
Since the emf is negative, it means that the induced current will flow in the opposite direction to the change in magnetic field.
Approximating π ≈ 3.14, the induced emf is approximately:
emf ≈ -0.00008(3.14) V
≈ -0.0002512 V
Therefore, the induced emf in the loop when the radius is 2 cm is approximately -0.0002512 V, or -251.2 μV.
emf = -dφ/dt
where emf is the induced electromotive force, dφ is the change in magnetic flux, and dt is the change in time.
The magnetic flux through the loop is given by:
Φ = B⋅A
where B is the magnetic field strength and A is the area of the loop.
Since the loop is circular and its plane is perpendicular to the magnetic field, the area of the loop remains constant as the radius shrinks.
Therefore, the change in magnetic flux is simply the product of the change in magnetic field and the constant area:
dΦ/dt = B⋅dA/dt
Since dA/dt is the rate at which the area changes with time, and the radius is shrinking at 2 mm/s, we have:
dA/dt = -2πr(dr/dt)
where r is the radius of the loop.
Substituting this expression into the equation for the change in magnetic flux, we get:
dΦ/dt = -2πr(dr/dt)B
Now we can substitute this expression into Faraday's law of electromagnetic induction to find the induced emf:
emf = -dΦ/dt
= -(-2πr(dr/dt)B)
= 2πr(dr/dt)B
Substituting the given values of r = 2 cm = 0.02 m, dr/dt = -2 mm/s = -0.002 m/s, and B = 0.04 T, we can calculate the induced emf:
emf = 2π(0.02)(-0.002)(0.04)
= -0.00008π V
Since the emf is negative, it means that the induced current will flow in the opposite direction to the change in magnetic field.
Approximating π ≈ 3.14, the induced emf is approximately:
emf ≈ -0.00008(3.14) V
≈ -0.0002512 V
Therefore, the induced emf in the loop when the radius is 2 cm is approximately -0.0002512 V, or -251.2 μV.
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A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm isa)4.8 π μVb)0.8 π μVc)1.6 π μVd)3.2 π μVCorrect answer is option 'D'. Can you explain this answer?
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A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm isa)4.8 π μVb)0.8 π μVc)1.6 π μVd)3.2 π μVCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm isa)4.8 π μVb)0.8 π μVc)1.6 π μVd)3.2 π μVCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm isa)4.8 π μVb)0.8 π μVc)1.6 π μVd)3.2 π μVCorrect answer is option 'D'. Can you explain this answer?.
A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm isa)4.8 π μVb)0.8 π μVc)1.6 π μVd)3.2 π μVCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm isa)4.8 π μVb)0.8 π μVc)1.6 π μVd)3.2 π μVCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm isa)4.8 π μVb)0.8 π μVc)1.6 π μVd)3.2 π μVCorrect answer is option 'D'. Can you explain this answer?.
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