Electromagnectic Induction

# Electromagnectic Induction - Electromagnetic Induction...

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Electromagnetic Induction PHY232 Remco Zegers [email protected] Room W109 – cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html

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PHY232 - Remco Zegers Electromagnetic Inductions 2 previously: ¾ electric currents generate magnetic field. If a current is flowing through a wire, one can determine the direction of the field with the (second) right-hand rule: ¾ and the field strength with the equation: B= μ 0 I/(2 π R) ¾ For a solenoid or a loop (which is a solenoid with one turn): B= μ 0 IN/(2R) (at the center of the loop) If the solenoid is long: B= μ 0 In (at the center of the solenoid)
PHY232 - Remco Zegers Electromagnetic Inductions 3 now: ¾ The reverse is true also: a magnetic field can generate an electrical current ¾ This effect is called induction : In the presence of a changing magnetic field, and electromotive force (voltage) is produced. demo: coil and galvanometer Apparently, by moving the magnet closer to the loop, a current is produced. If the magnet is held stationary , there is no current.

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PHY232 - Remco Zegers Electromagnetic Inductions 4 a definition: magnetic flux ¾ A magnetic field with strength B passes through a loop with area A ¾ The angle between the B-field lines and the normal to the loop is θ ¾ Then the magnetic flux Φ B is defined as: Units: Tm 2 or Weber (W) lon-capa uses Wb
PHY232 - Remco Zegers Electromagnetic Inductions 5 example: magnetic flux ¾ A rectangular-shaped loop is put perpendicular to a magnetic field with a strength of 1.2 T. The sides of the loop are 2 cm and 3 cm respectively. What is the magnetic flux? ¾ B=1.2 T, A=0.02x0.03=6x10 -4 m 2 , θ =0. ¾ Φ B =1.2 x 6x10 -4 x 1 = 7.2x10 -4 Tm ¾ Is it possible to put this loop such that the magnetic flux becomes 0? ¾ a) yes ¾ b) no answer: yes if the angle θ is zero

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PHY232 - Remco Zegers Electromagnetic Inductions 6 Faraday’s law: ¾ By changing the magnetic flux ΔΦ B in a time-period Δ t a potential difference V (electromagnetic force ε ) is produced Warning: the minus sign is never used in calculations. It is an indicator for Lenz’s law which we will see in a bit.
PHY232 - Remco Zegers Electromagnetic Inductions 7 changing the magnetic flux ¾ changing the magnetic flux can be done in 3 ways: ¾ change the magnetic field ¾ change the area ¾ changing the angle

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PHY232 - Remco Zegers Electromagnetic Inductions 8 example x x x x x x x x x x x x ¾ a rectangular loop (A=1m 2 ) is moved into a B-field (B=1 T) perpendicular to the loop, in a time period of 1 s. How large is the induced voltage? The field is changing: V=A Δ B/ Δ t=1x1/1=1 V While in the field (not moving) the area is reduced to 0.25m 2 in 2 s. What is the induced voltage? The area is changing by 0.75m 2 : V=B Δ A/ Δ t=1x0.75/2=0.375 V This new coil in the same field is rotated by 45 o in 2 s. What is the induced voltage?
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Electromagnectic Induction - Electromagnetic Induction...

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