The Electric Field The Electric Field n n

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The Electric Field

The Electric Field

The Electric Field n n Similar to a gravitational field. An Electric Field exists

The Electric Field n n Similar to a gravitational field. An Electric Field exists in a region of space if an electric force is exerted on a charged particle.

The Electric Field n This idea, known as action at a distance, is illustrated

The Electric Field n This idea, known as action at a distance, is illustrated below: • Problem is there is know way to explain how one charge “knows” that another charge is near it. n Assumes one charge (q 1) somehow changes the space around it. A second charge (q 2) then interacts with the field with the result that a force is exerted on this charge. +q 1 F -q 2

Electric Field Lines (Lines of Force) n § Field Lines, also called lines of

Electric Field Lines (Lines of Force) n § Field Lines, also called lines of force, are models that we create in order to visualize an electric field. A field line is the path that a very small positive charge (known as a test charge) takes while in the field. § A negative charge would move along the same field line but in the opposite direction.

Electric Field Lines (Lines of Force) n Diagrams representing electric field of positive and

Electric Field Lines (Lines of Force) n Diagrams representing electric field of positive and negative charges on overhead • Notice the fields have a great deal of symmetry associated with them. • The number of lines is an indication of the magnitude of the charge. • The spacing (or concentration) of the field lines indicates the relative strength of the field.

Electric Field Lines (Lines of Force) n n Diagram two equal and opposite charges

Electric Field Lines (Lines of Force) n n Diagram two equal and opposite charges placed near each other (known as a dipole) Diagram two positive (like) charges placed near each other. • Notice no field lines pass through the midway point between the charges. • If a charge were placed at that point, it would experience no net force. The field strength is zero at that point.

Electric Field Lines (Lines of Force) n n Diagram field lines between two oppositely

Electric Field Lines (Lines of Force) n n Diagram field lines between two oppositely charged parallel plates. Diagram field lines inside a hollow conductor. • Note no electric field exists inside the conductor. n Demo - cell phones

Electric Field Strength n The Electric Field is a vector quantity • Makes sense…

Electric Field Strength n The Electric Field is a vector quantity • Makes sense… our diagrams had arrows indicating direction. n To measure the strength, we take a very small positive test charge, place it in the field, and measure the force on it. • Diagram

Electric Field Strength n § We define the strength of the field as the

Electric Field Strength n § We define the strength of the field as the ratio of the force (F) to the magnitude of the test charge (qo) E = F/qo (reference tables) We divide by the test charge so that the result (E) depends on the charge (or charges) producing the field, not on the test charge itself.

Sample Problem n A test charge of +2. 0 x 10 -6 coulomb experiences

Sample Problem n A test charge of +2. 0 x 10 -6 coulomb experiences a force of 2. 4 x 10 -3 newton [east] when placed in an electric field. Determine the magnitude and direction of the electric field.

Mini-Activity Intro to Potential Difference

Mini-Activity Intro to Potential Difference

Potential Difference n We can also describe the electric field in terms of work

Potential Difference n We can also describe the electric field in terms of work and energy. n Consider the diagram on the board… • Say we move test charge qo between points A and B in an electric field. • If the charge is repelled by the field, then we must do work to move it between the two points. • The work we do against the field (WAB) will increase the potential energy of the test charge.

Electrical Energy and Electrical Potential Two completely different things that sound alike! n In

Electrical Energy and Electrical Potential Two completely different things that sound alike! n In order to bring two like charges near each other work must be done. In order to separate two opposite charges, work must be done. Remember that whenever work gets done, energy changes form.

Potential Difference n n Another way of describing this situation is to say that

Potential Difference n n Another way of describing this situation is to say that a potential difference exists between points A and B in the electric field. We define this potential difference (VAB) as follows: VAB = WAB / qo (reference tables)

Potential Difference n n Potential difference is a scalar quantity, as is work. The

Potential Difference n n Potential difference is a scalar quantity, as is work. The unit of potential difference is the joule per coulomb called the volt.

Sample Problem n When a charge of -4 x 10 -3 coulomb is moved

Sample Problem n When a charge of -4 x 10 -3 coulomb is moved between two points in an electric field, 0. 8 joule of work is done on the charge. Calculate the potential difference between the two points.

The “electron-volt” n Now let’s calculate the work done on an elementary charge that

The “electron-volt” n Now let’s calculate the work done on an elementary charge that is moved between two points in an electric field with a potential difference of 1 volt…. W=q. V (rearranged our equation) W = (1. 60 x 10 -19 C) (1. 0 V) = 1. 60 x 10 -19 J

The “electron-volt” n n This very small quantity of work (energy) is frequently used

The “electron-volt” n n This very small quantity of work (energy) is frequently used as a unit of energy in atomic and nuclear physics. It is known as the electron-volt.

Sample Problem n A charge equal to 2 x 107 elementary charges is moved

Sample Problem n A charge equal to 2 x 107 elementary charges is moved through a potential difference of 3000 volts. What is the change in the potential energy of the charge? W = q. V = (2 x 107 el. ch. ) (3000 V) = 6 x 1010 e. V = 60 Ge. V

Electric Potential n n We now know its possible to measure the potential difference

Electric Potential n n We now know its possible to measure the potential difference between two points A and B. What if we want to know the electric potential at just one of these points? How can we accomplish this?

Electric Potential n n Situation is similar to climbing a hill vertically. Secret is

Electric Potential n n Situation is similar to climbing a hill vertically. Secret is to establish a reference point whose value is zero. • In the case of elevation, we often choose sea level, with a height of 0 meters, as the reference point.

Electric Potential n n Similarly, to assign electric potentials, we establish a reference point

Electric Potential n n Similarly, to assign electric potentials, we establish a reference point of 0 volts. For an isolated charge, the reference point is taken to be infinitely far from the charge. • In some cases, the ground may be taken as a reference point.

Electric Potential n n We can now measure the potential difference between the point

Electric Potential n n We can now measure the potential difference between the point in question and the reference point, and assign this value as the electric potential of the point. The electric potential at a point is defined as the work needed to move a charge of 1 coulomb from infinity to the point in question.

Electric Potential VA∞ = 36 V A VA = 36 V ∞ V∞ =

Electric Potential VA∞ = 36 V A VA = 36 V ∞ V∞ = 0 V

Field Strength and Potential Difference n Diagram – parallel plates (overhead) W = (Fapplied)

Field Strength and Potential Difference n Diagram – parallel plates (overhead) W = (Fapplied) d = (V) (qo) F = (E) (qo) = Fapplied Combining gives… (E) (d) = (V) or E=V/d

Sample Problem n n Calculate the uniform electric field between two parallel plates if

Sample Problem n n Calculate the uniform electric field between two parallel plates if the potential difference between them is 50. volts and they are 2. 5 mm apart. Solution • E = V/d = (50. V) / (2. 5 x 10 -3 m) • E = 2. 0 x 104 V/m • Note that V/m are equivalent to N/C