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Electric and Magnetic Fields. Chapters 17 & 21. Electric Field. 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
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Electric and Magnetic Fields Chapters 17 & 21
Electric Field • 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 • A charged object has an electric field in the space around it
Electric Field Lines • 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 electric field is strong where the field lines are close together and weaker when they are far apart
Electric Field Lines The lines for a positive charge point away from the charge The lines for a negative charge point towards the charge
Electric Field Lines • 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
Electric Field Lines • 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
Electric Field Lines • 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
Calculating Electric Field Strength • The equation for the electric field produced by a point charge is: • Kc=9x109 Nm2/C2 ,r is the distance from the charge and q is the charge producing the field • The unit for E is N/C • Electric field strength is a vector!! • If q is positive, then E is directed away from q • If q is negative, then E is directed toward q
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 Remember that F is a vector!!
Sample Problem p. 647 #3 • An electric field of 2.0 x 104 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?
Sample Problem p. 647 #3 E field + • E= 2.0 x 104 N/C , q= 1.6 x 10-19 C • F=qE= 3.2 x 10-15 N for both the electron and the proton • 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
For the proton F + + 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)
- F + 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 • Answer: 3.2 x 10-15 N along the negative x axis (to the left)
+30 nC +60 nC 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
+30 nC +60 nC Sample Problem p. 656 #38 • For the 30 nC charge: • Direction of the E-field for both charges is “away” since they’re both positive • For the 60 nC charge:
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. 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
Sample Problem (p.659 #66) • A constant electric field directed along the positive x-axis has a strength of 2.0 x 103 N/C. • Find the electric force exerted on a proton by the field • Find the acceleration of the proton
F + E field + Answer • F=qE=(1.6x10-19 C)(2.0 x 103 N/C)= • 3.2 x 10-16 N • Direction? Answer: 3.2 x 10-16 N along the positive x-axis (to the right)
Answer • B. What is the acceleration? • Ask Newton! • F=ma • a = F/m= 3.2 x 10-16 N/1.6x10-27 kg • a= 2 x 1011 m/s2 along the positive x axis
Magnets • The ends of a bar magnet are called poles • Like poles repel and unlike poles attract • Regardless of their shape, all magnets have a north and south pole
Magnetic Fields • 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)
Magnetic Field of the Earth • 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
Magnetic Field of a wire Moving charges produce magnetic fields If there is a current moving through a wire, a magnetic field is produced around the wire
Magnetic Field of a wire 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
Magnetic 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)
A second Right-Hand Rule • Of course, force is a vector! • To find the direction of the magnetic force use another right hand rule • Fingers point in direction of the field • Thumb points in direction of v • Palm points in direction of magnetic force
Conventions for direction of field 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!
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?
The speed of the proton • What’s the direction of F? Use the RHR!! • v is east, B is north…F is…. • Out of the page! • If it was an electron, the force would be into the page!
Sample Problem (not in book) • An electron is moving with a velocity of 6 x 106 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.
Sample Problem (not in book) • F= 2.88 x 10-12 N • Direction? Use the RHR • V points west, B points out of the page… • F points SOUTH (remember it’s an electron!!)