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Electric and Magnetic Fields Chapters 17 & 21

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Electric Field Electric force, like gravitational force, is a field force Electric force, like gravitational force, is a field force Remember: Field forces can act through space even when there is no physical contact between the objects involved Remember: Field forces can act through space even when there is no physical contact between the objects involved A charged object has an electric field in the space around it A charged object has an electric field in the space around it

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Electric Field Lines Electric Field Lines point in the direction of the electric field Electric Field Lines point in the direction of the electric field The number and spacing of field lines is proportional to the electric field strength The number and spacing of field lines is proportional to the electric field strength The electric field is strong where the field lines are close together and weaker when they are far apart The electric field is strong where the field lines are close together and weaker when they are far apart

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Electric Field Lines The lines for a positive charge point away from the charge The lines for a positive charge point away from the charge The lines for a negative charge point towards the charge The lines for a negative charge point towards the charge

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Electric Field Lines This diagram shows the electric field lines for two equal and opposite point charges This diagram shows the electric field lines for two equal and opposite point charges Notice that the lines begin on the positive charge and end on the negative charge Notice that the lines begin on the positive charge and end on the negative charge

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Electric Field Lines This diagram shows the electric field lines for two positive point charges This diagram shows the electric field lines for two positive point charges Notice that the same number of lines emerges from each charge because they are equal in magnitude Notice that the same number of lines emerges from each charge because they are equal in magnitude

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Electric Field Lines If the charges are unequal, then the number of lines emerging from them will be different If the charges are unequal, then the number of lines emerging from them will be different Notice that the positive charge has twice as many lines Notice that the positive charge has twice as many lines

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Calculating Electric Field Strength The equation for the electric field produced by a point charge is: The equation for the electric field produced by a point charge is: K c =9x10 9 Nm 2 /C 2,r is the distance from the charge and q is the charge producing the field K c =9x10 9 Nm 2 /C 2,r is the distance from the charge and q is the charge producing the field The unit for E is N/C The unit for E is N/C Electric field strength is a vector!! Electric field strength is a vector!! If q is positive, then E is directed away from q If q is positive, then E is directed away from q If q is negative, then E is directed toward q If q is negative, then E is directed toward q

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Calculating the force from an electric field If a charged object is placed in an electric field, we can calculate the force acting on it from the electric field If a charged object is placed in an electric field, we can calculate the force acting on it from the electric field Remember that F is a vector!! Remember that F is a vector!!

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Sample Problem p. 647 #3 An electric field of 2.0 x 10 4 N/C is directed along the positive x-axis An electric field of 2.0 x 10 4 N/C is directed along the positive x-axis a. What is the electric force on an electron in this field? b. What is the electric force on a proton in this field?

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Sample Problem p. 647 #3 E= 2.0 x 10 4 N/C, q= 1.6 x 10 -19 C E= 2.0 x 10 4 N/C, q= 1.6 x 10 -19 C F=qE= 3.2 x 10 -15 N for both the electron and the proton F=qE= 3.2 x 10 -15 N for both the electron and the proton What about the direction? What about the direction? The electric field is pointing along the positive x axis (to the right) which means there’s a positive charge to the left The electric field is pointing along the positive x axis (to the right) which means there’s a positive charge to the left E field +

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For the proton Since the electric field is pointing to the right, if you put a proton in it, the proton will want to move away towards the right and the direction of the force on it will be to the right Since the electric field is pointing to the right, if you put a proton in it, the proton will want to move away towards the right and the direction of the force on it will be to the right Answer: 3.2 x 10 -15 N along the positive x axis (to the right) Answer: 3.2 x 10 -15 N along the positive x axis (to the right) + + F

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For the electron Since there’s a positive charge causing the electric field to point towards the right, an electron would feel attracted to the positive charge. Therefore, the force acting on it is toward the left Since there’s a positive charge causing the electric field to point towards the right, an electron would feel attracted to the positive charge. Therefore, the force acting on it is toward the left Answer: 3.2 x 10 -15 N along the negative x axis (to the left) Answer: 3.2 x 10 -15 N along the negative x axis (to the left) + - F

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Sample Problem p. 656 #38 Find the electric field at a point midway between two charges of +30 nC and 60 nC separated by a distance of 30.0 cm Find the electric field at a point midway between two charges of +30 nC and 60 nC separated by a distance of 30.0 cm +30 nC+60 nC

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Sample Problem p. 656 #38 For the 30 nC charge: For the 30 nC charge: Direction of the E-field for both charges is “away” since they’re both positive Direction of the E-field for both charges is “away” since they’re both positive For the 60 nC charge: For the 60 nC charge: +30 nC+60 nC

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Which one will win? At the midway point, the 30nC charge’s field strength is 12000 N/C toward the 60 nC charge and the 60 nC charge’s field strength is 24,000 N/C toward the 30 nC charge. At the midway point, the 30nC charge’s field strength is 12000 N/C toward the 60 nC charge and the 60 nC charge’s field strength is 24,000 N/C toward the 30 nC charge. The 60 nC charge will win. Since the field’s point in opposite directions, you have to subtract The 60 nC charge will win. Since the field’s point in opposite directions, you have to subtract Answer: 12,000 N/C toward the 30 nC charge Answer: 12,000 N/C toward the 30 nC charge

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Sample Problem (p.659 #66) A constant electric field directed along the positive x-axis has a strength of 2.0 x 10 3 N/C. A constant electric field directed along the positive x-axis has a strength of 2.0 x 10 3 N/C. Find the electric force exerted on a proton by the field Find the electric force exerted on a proton by the field Find the acceleration of the proton Find the acceleration of the proton

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Answer Answer F=qE=(1.6x10 -19 C)(2.0 x 10 3 N/C)= F=qE=(1.6x10 -19 C)(2.0 x 10 3 N/C)= 3.2 x 10 -16 N 3.2 x 10 -16 N Direction? Direction? Answer: 3.2 x 10 -16 N along the positive x-axis (to the right) E field + + F

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Answer Answer B. What is the acceleration? B. What is the acceleration? Ask Newton! Ask Newton! F=ma F=ma a = F/m= 3.2 x 10 -16 N/1.6x10 -27 kg a = F/m= 3.2 x 10 -16 N/1.6x10 -27 kg a= 2 x 10 11 m/s 2 along the positive x axis a= 2 x 10 11 m/s 2 along the positive x axis

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Magnetism!

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Magnets The ends of a bar magnet are called poles The ends of a bar magnet are called poles Like poles repel and unlike poles attract Like poles repel and unlike poles attract Regardless of their shape, all magnets have a north and south pole Regardless of their shape, all magnets have a north and south pole

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Magnetic Fields Magnetic Field lines point from the north pole to the south pole of the magnet Magnetic Field lines point from the north pole to the south pole of the magnet The north pole of a compass needle always points in the direction of the field (from North to South) The north pole of a compass needle always points in the direction of the field (from North to South)

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Magnetic Field of the Earth The Earth’s geographic North pole is actually the magnetic south pole The Earth’s geographic North pole is actually the magnetic south pole The north pole of a compass points towards geographic north and since opposites attract, we know that the Earth’s geographic pole is magnetic south The north pole of a compass points towards geographic north and since opposites attract, we know that the Earth’s geographic pole is magnetic south

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Magnetic Field of a wire Moving charges produce magnetic fields Moving charges produce magnetic fields If there is a current moving through a wire, a magnetic field is produced around the wire If there is a current moving through a wire, a magnetic field is produced around the wire

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Magnetic Field of a wire The “Right Hand Rule” for the magnetic field The “Right Hand Rule” for the magnetic field Point your thumb in the direction of the current and curl your fingers in the direction of the field Point your thumb in the direction of the current and curl your fingers in the direction of the field

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Magnetic Force A charge moving through a magnetic field experiences a force A charge moving through a magnetic field experiences a force q= magnitude of charge v= speed of charge B= Strength of the magnetic field (measured in Tesla, T)

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A second Right-Hand Rule Of course, force is a vector! Of course, force is a vector! To find the direction of the magnetic force use another right hand rule To find the direction of the magnetic force use another right hand rule Fingers point in direction of the field Fingers point in direction of the field Thumb points in direction of v Thumb points in direction of v Palm points in direction of magnetic force Palm points in direction of magnetic force

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Conventions for direction of field Conventions for direction of field Direction of Field Symbol Into the page X Out of the page WARNING: The right hand rule is for the direction of the force acting on a POSITIVE CHARGE. To find the direction of the force acting on a negative charge, you’ll have to use the rule and change the sign!

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Examples Direction of FDirection of vDirection of BSign of Charge Out of the pageEastNorth+ Into the pageEastNorth- Out of the pageWestSouth+ Into the pageWestSouth- WestInto the page+ SouthWestOut of the page- EastNorthOut of the page+ SouthOut of the pageEast- Out of the pageSouthWest- Into the pagewestNorth+

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Sample Problem p. 775 #2 (edited) A proton traveling to the right along the x-axis enters a region where there is a magnetic field of 2.5 T directed north. If the proton experiences a force of 3.2 x 10 -12 N, find the speed of the proton. What is the direction of the force exerted on the proton? A proton traveling to the right along the x-axis enters a region where there is a magnetic field of 2.5 T directed north. If the proton experiences a force of 3.2 x 10 -12 N, find the speed of the proton. What is the direction of the force exerted on the proton?

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The speed of the proton What’s the direction of F? Use the RHR!! What’s the direction of F? Use the RHR!! v is east, B is north…F is…. v is east, B is north…F is…. Out of the page! Out of the page! If it was an electron, the force would be into the page! If it was an electron, the force would be into the page!

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Sample Problem (not in book) An electron is moving with a velocity of 6 x 10 6 m/s westward in a 3.0 T magnetic field that is pointed out of the page. An electron is moving with a velocity of 6 x 10 6 m/s westward in a 3.0 T magnetic field that is pointed out of the page. Find the magnitude and direction of the force acting on the electron. Find the magnitude and direction of the force acting on the electron.

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Sample Problem (not in book) F= 2.88 x 10 -12 N F= 2.88 x 10 -12 N Direction? Use the RHR Direction? Use the RHR V points west, B points out of the page… V points west, B points out of the page… F points SOUTH (remember it’s an electron!!) F points SOUTH (remember it’s an electron!!)

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