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All motion is relative. If a charge moves within wire, a magnetic field is created around the wire. Likewise, if a magnet field moves near wire, an emf (electro motive force) is INDUCED.
INDUCED: to produce, or cause, by proximity without contact or transmission, as a particular electric or magnetic condition in a body, by the approach of another body in an opposite electric or magnetic state.
A key aspect of Faraday's Law is Magnet FLUX (Φ), the amount of magnetic field (B) passing through a specific area (A). Equation a. below
The area is typically the area of a loop of wire. To increase efficiency the wires are looped into a device called a SOLENOID. The number of loops (N) increases the Flux and is referred to as FLUX LINKAGE (eq. b.). Because they are so tightly linked both Flux and Flux Linkage are both designated with the variable Φ (Phi).
FLUX Sample Problem:
FLUX Sample Problem:
A loop of 2 cm2 is in a constant magnetic field of B = 0.10 T. What is the magnetic flux through the loop when:
the loop is perpendicular to the field; ∴Area exposed to the field is 0m2 θ = 90˚ ∴ ɸ = 0 Wb
the loop is parallel to the field; ∴Area exposed to the field is 2cm2. θ = 0˚ ∴ ɸ = 2 x 10-5 Wb
the normal to the loop and field have an angle of 60˚ between them? θ = 30˚ ∴ ɸ = 1.7 x 10-5 Wb
The magnetic flux passing through 10 circular loops each with a radius of 0.04 cm is measured at 2.5 x 10-4 Wb, when the magnetic flux is normal to the loops. Determine the magnetic field strength passing through the solenoid (10 coils). B = 5.0 T
Faraday's Law - Everything BUT the Negative Sign
Faraday's Law - Everything BUT the Negative Sign
The current produced will depend upon the following:
Faraday found that the induced emf depended of any of the following:
the relative speed of the magnet with respect to the coil (v)
the strength of the magnetic field (B)
the number of turns in the solenoid (N)
the cross-sectional area of the solenoid (A)
the angle between the magnetic field and the solenoid (θ) (max at 90˚)
(a) When this bar magnet is thrust into the coil, the strength of the magnetic field increases in the coil. The current induced in the coil creates another field, in the opposite direction of the bar magnet’s to oppose the increase. This is one aspect of Lenz’s law—induction opposes any change in flux. (b) and (c) are two other situations. - OpenStax College Physics for AP
Sample Problems
Sample Problems
The magnetic field through a single loop of area 0.2 m2 is changing at the rate of 4 T s-1. Determine the induced emf. N = 1, A = 0.2, ΔΒ/Δt = 4 T s-1 ∴ emf = 0.8 V
The setup in the previous problem is repeated but with a similar solenoid of unknown coils. The emf produced is 80V. Determine the number of coils in the solenoid. emf = 80V, A = 0.2, ΔΒ/Δt = 4 T s-1 ∴ N = 100 coils.
Bouncing Magnets and Voltages
Bouncing Magnets and Voltages
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