Approximating changes Approximate the change in the magnitude of the electrostatic force between two charges when the distance between them increases from ?r? = 20 m to r ? ? = 21 m (?F?(?r?) = 0.01/r2).
Solution 28E STEP 1 According to the approximation formula we can write f(x + x) f(x) = f(x).x f = f x).x, Where f is the function,x is the variable and x is the change in x. STEP 2 Therefore according to this question, we have to approximate the change in the magnitude of the electrostatic force between 2 charges when the distance between them increases from r=20m to r=21m F(r) = 0.01 r STEP 3 The electrostatic force between 2 charges with r as the distance between them is given by F(r) = 0.01 F (r) = 2 × 0.01= 0.02 r2 r r3 Thus according to the equation ,we write F = F (r.r......................(1) Here r=20 m and r = 21 20 = 1m (1) 0.02 F = F (rr = 203 × 1 = 0.0000025 F = 0.0000025m 3 Thus the change in F , F = 0.0000025m 3