Lecture%2020C - Physics 1B Lecture 20C Electrical potential...

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Unformatted text preview: Physics 1B Lecture 20C Electrical potential: superposition Electrical potential due to a single point (or spherical) charge, assuming that the potential at infinity is zero What is the potential due to two (or a set of N) of point charges? Potentials due to individual charges add algebraically (where r 1 , r 1 , …) are distances between the chanregs and the point where we measure the potential, V. r q k V e = 2 2 1 1 2 1 r q k r q k V V V e e Tot + = + = ∑ + + + = N Tot V V V V ... 2 1 Superposition of potentials Example: Calculate the total potential in the center of a square with a side of 1 m and charges in the corners: 3.0μC (top left), 2.0μC (bottom left), 1.0μC (bottom right), and -1.0μC (top right). Answer First, you must define a coordinate system. Let’s choose up as the +y direction and to the right as the +x direction and the origin in the center. 1.0m q 1 =+3.0μC +x 1.0m 1.0m 1.0m q 2 =+2.0μC q 3 =1.0μC q 4 =-1.0μC +y Superposition Answer Let’s list the quantities we know: q 1 = +3.0x10 –6 Coul q 2 = +2.0x10 –6 Coul q 3 = +1.0x10 –6 Coul q 4 = –1.0x10 –6 Coul r 1 = r 2 = r 3 = r 4 = 0.71m Instead of calculating the individual potentials separately, we can use the fact that all distances are the same and write the equation for the total potential: 1.0 1.0 45 o m 71 . 2 / 2 = = r 4 4 3 3 2 2 1 1 4 3 2 1 r q k r q k r q k r q k V V V V V e e e e Tot + + + = + + + = Superposition ) ( 4 3 2 1 4 3 2 1 q q q q r k r q k r q k r q k r q k V e e e e e Tot + + + = + + + = ) 10 1 10 1 10 2 10 3 ( 71 . / 10 9 6 6 6 6 2 2 9 C C C C m C Nm Tot − − − − × − × + × + × × = V C m C Nm V Tot 4 6 2 2 9 10 4 . 6 ) 10 5 ( 71 . / 10 9 × = × × = − Capacitors Capacitance, C, is a measure of how much charge can be stored for a capacitor with a given electric potential difference. Δ V For a parallel-plate capacitor we just drew, the capacitance is: where A is the area of one of the plates and d is the separation distance between the plates Circuits For example, let’s say that we had two capacitors connected in parallel to a battery....
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Lecture%2020C - Physics 1B Lecture 20C Electrical potential...

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