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capa2-question14

# capa2-question14 - Problem 5 13.61:1 Line at" positive...

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Unformatted text preview: Problem 5: 13.61 :1 Line at" positive charge is famed iJJIcI a semicircle ufradius E— ISIZLIZI cm. as. sham: in Figure P23.ﬁl. The rJnge per unit length along the semicircle is. described hf the expression A —Ancu5\$. The total charge on ﬁle semicircle l5 llﬂyf . Calculate the total force an. a charge at" 3.IZIU_HC placed at [he center of cur'La‘mre. Salutinl: Denote thu hethe charge atthe center amiq mhe ﬁle total charge an [he semicircle: [has weha'i'e ﬁnccthe ﬁncccethat each diﬂ'erential d'q exectw ﬁle ceuna] charge is .i: :iF — ‘9qu (1.19] R n‘e Hcrwet'ec, we kmw that - A..cursr5':th1:5 1 ﬁg - A". coeﬁ'n‘f - A". cueﬁ'ﬁa‘ﬁ‘ (1.21)] Also: if we consider [be whole semicircle of charge, we see that the x—cumponent cut" the recultamfulce would he 2&7th symmetry, 50 [ﬂat er, 329m, msexde‘lcnse—Lg'j" comer; (1.21] R. a , R Integrating: we get 329% = Fl _ H Lﬁms am;- (1.22] which gives 1' r, _ I '9‘ (1.231 2:: Ncrw we have to solve Eur J1..Ifwe integrate hot side of {1.20}. we can get 4-34.. image—emu (1.24] _2 . *i‘ . . we get A” —E and thus: Slab-511mg to {1.23}: 2121)} Spring 3.1): with Kai Problem Set I Solution '? :rkaq 43:: (1.25] which gives 1-: _ tum r; (1.25] ...
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capa2-question14 - Problem 5 13.61:1 Line at" positive...

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