(1+x) m =1+? ? n=1 (m(m?1)(m?2)...(m?n+1)x n )/n! a) In this problem we will exa
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(1+x) m =1+? ? n=1 (m(m?1)(m?2)...(m?n+1)x n )/n! a) In this problem we will examine an "electric dipole". Many systems can be viewed as equal and opposite electric charges separated by some distance. Thus, it is important to understand their cumulative electrical effect on their surroundings. Using a = 0.1m and d = 1m, determine the ent force on q. Now repreat but use d =2m. By what factor did the net force change? Explain b) Now use the binomial theorem to expand the force rom each charge in the dipole in terms of a/2d. show that after adding the forces due to each charge that the first remaingin term depends upon 1/d^3. Here is the binomial expansion if /x/ <1.Explanation / Answer
Equation is: (n 0) + (n 1) + ... = 2^n For n = 0, (n 0) = (0 0) = 0!/(0!)^2 = 1 = 2^0 [0! is taken as 1] For n = 1, (n 0) + (n 1) = (1 0) + (1 1) = 2^1 Say this holds upto n = m. So this holds for n = m-1,m-2... Hence (m 0) + (m 1) + ... + (m m) = 2^m (n+1 r) = (n r) + (n r-1) for r>=1 and rRelated Questions
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