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02_21_E_Field_1

# 02_21_E_Field_1 - E q = kQ s/r 2 = k(q o(r o 2 = E o...

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Today 2/21 o E-Field and Coulomb’s Law 18.4-5 o Examples o HW: “2/21 2-D E Field ” Due Wednesday 2/26

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Many Charge Example (Like HW) E = kQ s /r 2 Q 1 Q 2 Q 3 Each Square is r o on a side, Q 1 = -4 q o , Q 2 = +2 q o , Q 3 = -6 q o (See how this simplifies the math) Find the E field at Q 1 ’s location. E Q2,x = k Q s r 2 k 2 q o (4 r o ) 2 kq o r o 2 1 8 Up, (away from Q 2 ) E Q3,x = k Q s r 2 k 6 q o (6 r o ) 2 kq o r o 2 1 6 Down, (toward Q 3 ) Add vectors to get E net,x kq o r o 2 1 6 1 8 kq o r o 2 1 24 Down at the x F Others,q1 = q 1 E net,x q 1 kq o 2 r o 2 4 24
Many Charge Example (Like HW) E = kQ s /r 2 Q 1 Q 2 Q 3 Each Square is r o on a side, Q 1 = -4 q o , Q 2 = +2 q o , Q 3 = -6 q o (See how this simplifies the math) Find the E field at Q 2 ’s location. E Q1,x = k Q s r 2 k 4 q o (4 r o ) 2 kq o r o 2 1 4 Up, (toward Q 1 ) E Q3,x = k Q s r 2 k 6 q o (2 r o ) 2 kq o r o 2 3 2 Down, (toward Q 3 ) Add vectors to get E net,x kq o r o 2 3 2 1 4 kq o r o 2 5 4 Down at the x F Others,q2 = q 2 E net,x kq o 2 r o 2 5 2 q 2

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Many Charge Example E = kQ s /r 2 +q o -3q o +4q o -2q o r o What is the force on +4q o ? (direction also) Find the field at +4q o due to the “other” charges. These are the “source” charges.
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Unformatted text preview: E +q = kQ s /r 2 = k(q o )/(r o ) 2 = E o Direction? Away from + so right E-2q = kQ s /r 2 = k(2q o )/( √ 2r o ) 2 = E o = k2q o /2(r o ) 2 = k(q o )/(r o ) 2 E-3q = kQ s /r 2 = k(3q o )/(r o ) 2 = 3E o = 3kq o /(r o ) 2 Many Charge Example E = kQ s /r 2 +q o-3q o +4q o-2q o r o What is the force on +4q o ? (direction also) E +q = E o E-2q = E o E-3q = 3E o Now add E-Field vectors E x = E +q,x + E-2q,x E x = E o- E o sin45 E x = 0.29E o E y = E-2q,y + E-3q,y E y = E o sin45 + 3E o E y = 3.7E o θ = tan-1 (0.29/3.7) = 4.5° E total = √ 3.7 2 + 0.29 2 E o = 3.71E o F on +4q = (4q o )3.71E o = 14.84q o E o F on +4q = 14.84kq o 2 /r o 2 same direction as E total...
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02_21_E_Field_1 - E q = kQ s/r 2 = k(q o(r o 2 = E o...

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