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Find the magnetic induction of the field at the point O at a loop with current I, whose shape is illustrated in figure (a)In figure a the radii a and b, as well as the angle varphi are known (b)In figure b,the raidus a and the side b are known. (c)A current I=5.0 A flows along a thin wire shaped as shown in figure.The radius of a curved part of the wire is equal to R=120 mm,the angle 2varphi=90^(@).Find the magnetic induction of the field at the point O. |
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Answer» `B_("due to curved part AD")=((2pi-phi)/(2pi))((mu_(0)i)/(2a))` Into the plane of PAPER. `B_("due to curved part BC")=(phi)/(2pi)((mu_(0)i)/(2b))` Into the plane of paper. `B_(Net)=(mu_(0)i)/(4PI)[(2pi-phi)/a+phi/b]` Into the plane of paper. (b)`B_("due to BC")=B_("due to EA")=0` `B_("due to curved part AB")=((3pi)/2)/(2pi)(mu_(0)I)/(2a) rArr =3/8(mu_(0)l)/a` Into the plane of paper `B_("due to CD")=(mu_(0)i)/(4pib)[cos 90^(@)+cos 45^(@)]rArr=(mu_(0)I)/(4sqrt2pib)` Into the paper `B_("due to DE")=(mu_(0)I)/(4sqrt2pib)` Into the plane ofpaper `vecB_(Net)=(mu_(0)I)/(4pi)[(3pi)/(2a)-sqrt2/b]` Into the plane of paper. (c) `B=B_("due to st.part")+B_("due to curved part")` both into the plane of paper `=((2pi-2phi)/(2pi))(mu_(0)i)/(2R)+(mu_(0)i)/(4pid)[SIN phi+sin phi]` `=((2pi-2phi)/(2pi))(mu_(0)i)/(2R)+(mu_(0)i)/(4pi R cos phi)[2 sin phi]` `(mu_(0)i)/(2piR)[pi-phi+tanphi]=28muT`  
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