The Electric Field Physics for Scientists Engineers 2 For the past three days we have been discussing the force between two charges that we not moving with respect to each other Spring Semester 2005 Lecture 4 Suppose one charge were moving how would the second charge know that the first charge had moved What if there were other charges how would one charge know about the extra charges To deal with these situations we introduce the concept of a field January 12 2005 Physics for Scientists Engineers 2 1 January 12 2005 The Electric Field 2 We define the electric field in terms of the force it exerts on a positive point charge F E q The electric field is defined at any point in space as the force of the electric field on a positive point charge If we place a positive point charge in an electric field there will be a vector force on that charge in the direction of the electric field The magnitude of the force is given by the strength of the electric field Physics for Scientists Engineers 2 2 Definition of Electric Field A field is an abstract concept that we can use to describe forces January 12 2005 Physics for Scientists Engineers 2 The unit of the electric field are N C newtons per coulomb We can then write F qE We see that the electric force is parallel to the electric field and is proportional to the charge The force on a negative charge will be in the opposite direction 3 January 12 2005 Physics for Scientists Engineers 2 4 Superposition of Electric Fields Electric Field Lines Suppose we have many charges We can represent the electric field graphically by drawing lines that represent the vector force exerted on a positive test charge The electric field at any point in space will have contributions from all the charges The electric field at any point in space is the superposition of of the electric field from n charges is Electric field lines will originate on positive charges and terminate on negative charges Note that the superposition applies to each component of the field Electric field lines do not cross Electric fields exist in three dimensions but we often show a two dimension representation E E1 E2 E3 En January 12 2005 Physics for Scientists Engineers 2 The electric force at a given point in space is tangent to the electric field lines 5 Properties of Field Lines January 12 2005 Physics for Scientists Engineers 2 6 Field Lines from a Point Charge The strength of the electric field is represented by the density of electric field lines The electric field lines from a point charge extend out radially Weak For a positive point charge the field lines point outward Strong The direction of the electric field is tangent to the electric field lines Terminate at infinity For a negative charge the field lines point inward Originate at infinity January 12 2005 Physics for Scientists Engineers 2 7 January 12 2005 Physics for Scientists Engineers 2 8 Electric Field Lines for Two Point Charges Electric Field Lines from Identical Point Charges We can use the superposition principle to calculate the electric field from two point charges Now let s look at the electric field from two identical point charges Let s start with one positive charge and one negative charge The field lines will originate from the positive charge and terminate on the negative charge January 12 2005 Physics for Scientists Engineers 2 For two positive charges the field lines originate on the positive charges and terminate at infinity For two negative charges the field lines terminate on the negative charges and originate at infinity 9 January 12 2005 General Observations about Field Lines Physics for Scientists Engineers 2 10 Example Force from Field Lines If the field lines connect we have an attractive force You can imagine the charges pulling on each other What are the magnitudes high medium low and the direction of the electric force for the following four cases If the field lines seem to spread out we have a repulsive force 1 q at a You can imagine the charges pushing each other apart 3 q at c 2 q at b 4 q at d Field lines always originate on positive charge and terminate on negative charge d b a q q c Field lines never cross http lectureonline cl msu edu mmp kap18 RR447app htm January 12 2005 Physics for Scientists Engineers 2 11 January 12 2005 Physics for Scientists Engineers 2 12
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