Electromagnetic induction Objectives: 1.Describe what happens when a coil of wire is placed in a changing magnetic field. 2.Calculate the magnetic flux. 3.Calculate the induced EMF in a coil or a straight conductor. 4.Determine the direction of the induced current by applying Lenz’s law.

Electromagnetic induction is the production of a potential difference (voltage) across a conductor when it is exposed to a varying magnetic field.potential differenceconductormagnetic field Discovery was credited to Michael Faraday. Faraday’s law of electromagnetic induction states that any change in the magnetic environment of a coil of wire will cause a voltage (EMF) to be "induced" in the coil.

Magnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates.magnetic field  = ABcos   = magnetic flux in T·m 2 A = area of the coil in m 2 B = magnetic field in T  = angle between B and the area vector(an arrow drawn perpendicular to the plane of the coil)

 B  is the angle between B and the area vector (red arrow)

Induced EMF in a Coil  = - N   t = - N (  f -  i )  t = - N(A f B f cos  f – A i B i cos  i )  t  = induced electromotive force in V N = number of turns in the coil A= area of the coil in m 2 B = magnetic field  = magnetic flux in T·m 2  t = time is takes for the flux to change

xxxxxx B(in) xxxxxx xxxx vx xxxxxx Induced EMF in straight conductors

Induced EMF in straight conductor  = BLv  = induced electromotive force in V B = magnetic field in T L = length of the conductor in m v = speed of the conductor in m/s

Lenz’s law Remember the negative sign in the equation EMF = - N  ?  t The sign is explained by Lenz’s law.

Lenz’s law When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant.Faraday's Law

Personification of Lenz’s law Just as mass resists changes to its velocity, conducting hoops resist changes to the magnetic flux through them by creating their own flux to minimize the change.

Lenz’s law example Determine the direction of the current in the loop: XXXXXX B in is increasing

Answer Counter-clockwise Since the magnetic field is increasing in the direction into the page, the coil will create magnetic field that is directed out of the page to counter the change in the flux inside the coil. Using the second right hand rule, grab the coil such that your fingers are pointing the direction of the magnetic field (created by the coil) inside the coil and your thumb points to the direction of the current.

Lenz’s law example Determine the direction of the current in the loop: XXXXXX B in is decreasing

Answer Clockwise Since the magnetic field that is directed into the page is decreasing, the coil will create more magnetic field into the page to resist the decrease of the field into the page. Using the second right hand rule, grab the coil such that your fingers (magnetic field) are pointing into the page inside the coil. Your thumb (current) will then be pointing in the clockwise direction.

Lenz’s law example Determine the direction of the current in the loop: B out is increasing

Answer Clockwise Since the magnetic field is increasing out of the field, the loop will create a magnetic field into the page to resist the change. Using the second right hand rule, the fingers will point into the page inside the loop so the thumb is pointing in the clockwise direction.

Lenz’s law example Determine the direction of the current in the loop: B out is decreasing

Answer Counter-clockwise Since the magnetic field is decreasing out of the page, then the coil will create additional magnetic field out of the page to resist the decrease. Using the right hand rule, the fingers point out of the page inside the coil so the thumb is pointing counter-clockwise.

Lenz’s law example Determine the direction of the current in the loop: i increasing

Answer Counter-clockwise The magnetic field inside the loop due to the current in the vertical wire is increasing into the page. So the loop will create magnetic field inside the loop that is directed out of the page. With fingers pointing out of the page inside the loop, the thumb points in the counter-clockwise direction.

Lenz’s law example Determine the direction of the current in the loop: i decreasing

Answer Clockwise The magnetic field inside the loop due to the current in the vertical wire is decreasing into the page. The loop will then create more field into the page. Using the second right hand rule, fingers are pointing into the page inside the coil so the thumb is in the clockwise direction.