The Electric Field due to a Point Charge

The Electric Field due to a Point Charge - p. 11 The...

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O P 10 3.0 10 C q - = × 5.4 N/C 0.50 m r = p. 11 The Electric Field due to a Point Charge Consider a point charge q sitting in space. We shall call this charge (the charge that sets up an electric field) the source charge . Place a test charge q 0 at point P a distance r from the source charge. Remember that the test charge is always positive. The source charge can be either positive or negatively charged. An electrostatic force F acts on the test charge; this force can be computed using Coulomb’s law: 0 2 qq F k r = The electric field at P is given by 0 F E q = . Hence we can write 2 q E k r = . Note that q 0 cancels from the equation for E. Ex. Consider the table top of the previous examples. We assume the environment is the same as before, so at point P there is an electric field of 5.4 N/C directed upward. Now we place a small charge 10 3.0 10 C q - = × at point O 0.50 m to the left of P. Find the magnitude and direction of the resultant electric field at P. At point P: ( 29 y 2 10 9 x x 2 2 2 x E 5.4 N/C N m 3.0 10 C E ; E 8.99 10 C 0.50 m E 11 N/C q k r - = × = = × = ( 29 ( 29 2 2 1 1 E= 11 N/C 5.4 N/C E=12 N/C E 5.4 N/C Tan ; =Tan =26 E 11 N/C y x - - + θ = θ θ ° E = 12 N/C at 26 ° above the + x axis. The fact that we can “overlay” one electric field with another and obtain the resultant electric field using vector addition is called the principle of superposition . Electric and magnetic fields obey the principle of q q 0 r F P E y E x E y E x E θ Rev. 1/22/10
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p. 12 superposition. Not all fields, however, obey this principle. Strong gravitational fields (such as those near a black hole), for example, do not obey the principle of superposition. Weak gravitational fields (such as Earth’s), on the other hand, obey the principle of superposition to a good approximation. Permittivity of Free Space It is common practice to express the constant k that appears in Coulomb’s law in terms of another constant, 0 ε (epsilon zero): 0 1 4 k = πε . 0 ε
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The Electric Field due to a Point Charge - p. 11 The...

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