A circular loop of wire of radius 14 cm is placed in a magnetic field directed perpendicular to the plane of the loop as shown in the figure below. If the field decreases at the rate of 59 mT/s in some time interval, find the magnitude of the emf induced in the loop during this interval.(units of V)
Question
A circular loop of wire of radius 14 cm is placed in a magnetic field directed perpendicular to the plane of the loop as shown in the figure below. If the field decreases at the rate of 59 mT/s in some time interval, find the magnitude of the emf induced in the loop during this interval.(units of V)
Solution
To solve this problem, we need to use Faraday's Law of electromagnetic induction, which states that the induced emf in a closed loop is equal to the rate of change of magnetic flux through the loop.
The formula for Faraday's Law is:
emf = -dΦ/dt
where:
- emf is the induced electromotive force,
- dΦ/dt is the rate of change of magnetic flux.
The magnetic flux (Φ) through a loop is given by the product of the magnetic field strength (B), the area of the loop (A), and the cosine of the angle between the magnetic field and the normal to the loop (cosθ). In this case, the magnetic field is perpendicular to the loop, so θ = 0 and cosθ = 1.
So, Φ = B * A.
The area of a circle is given by πr², where r is the radius of the circle. In this case, the radius is 14 cm = 0.14 m, so the area is π * (0.14 m)² = 0.062 m².
The rate of change of the magnetic field strength is given as -59 mT/s = -59 * 10^-3 T/s.
So, the rate of change of magnetic flux is:
dΦ/dt = A * dB/dt = 0.062 m² * -59 * 10^-3 T/s = -0.00366 T*m²/s.
Substituting this into Faraday's Law gives:
emf = -(-0.00366 T*m²/s) = 0.00366 V.
So, the magnitude of the induced emf is 0.00366 V.
Similar Questions
A conducting circular loop is placed in a uniform magnetic field, B=0.025 TB=0.025 T with its plane perpendicular to the direction of the magnetic field. The radius of the loop is made to shrink at a constant rate of 1 mm s−11 mm s-1. Find the emf induced in the loop when it's radius is 2 cm2 cm.
A conducting loop of radius 10π√cm is placed perpendicular to a uniform magnetic field of 0.5T. The magnetic field is decreased to zero in 0.5s at a steady rate. The induced emf in the circular loop at 0.25s is:
A square loop of side 10 cm and resistance 0.7Ω is placed vertically in east-west plane. A uniform magnetic field of 0.20 T is set up across the plane in north east direction. The magnetic field is decreased to zero in 1 s at a steady rate. Then, magnitude of induced emf is x√×10−3 V. The value of x is _____
A circular loop in the plane of a paper lies in a 0.55 TT magnetic field pointing into the paper. The loop's diameter changes from 17.0 cmcm to 5.6 cmcm in 0.52 ss .Part APart completeWhat is the direction of the induced current?counterclockwiseclockwiseSubmitPrevious Answers CorrectPart BWhat is the magnitude of the average induced emf?
A 26-turn circular coil of wire has radius 0.4 m. It is placed with its axis along the direction of the Earth's magnetic field of 58.0 µT and then in 0.200 seconds is flipped 180°. An average emf of what magnitude is generated in the coil? (units of V)Answer
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.