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A long current wire is bent in the shapes shown in figure. The circular portion has radius R. The magnetic induction at the center of the circular segment is |
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Answer» `-(mu_(0)I)/(4piR)[2hat(k)p+pihat(i)],-(mu_(0)I)/(4piR)[hat(k)+(PI+1)hat(i)],-(mu_(0)I)/(4piR)[hat(k)+hat(j)+(3pi)/(2)hat(i)]`  Magnetic field due to segment ,`AB,` `overset(rarr)(B_(1))=(mu_(0)I)/(4piR)(-hat(k))` Magnetic field due to circular segment `BCD`, `overset(rarr)(B_(2))=(mu_(0)I)/(2R)xx((pi)/(2pi))(-hat(i))` Magnetic field due to segment `DE`, `overset(rarr)(B_(3))=(mu_(0)I)/(4piR)(-hat(k))` Resultant magnetic field, `vec(B_(3))=vec(B_(1))+vec(B_(2))+vec(B_(3))""=-(mu_(0)I)/(4piR)[2hat(k)+pihat(j)]` `(b)` Magnetic field due to segment `AB`, `vec(B_(1))=(mu_(0)I)/(4piR)(-hat(k))` Magnetic field due to circular segment BCD, `vec(B_(2))=(mu_(0)I)/(2R)((pi)/(2pi))(-hat(i))` Magnetic field due to segment DE, `vec(B_(3))=(mu_(0)I)/(4pir)(-hat(k))` Resultant magnetic field `vec(B_(R))=vec(B_(1))+vec(B_(2))+vec(B_(3))=-(mu_(0)I)/(4piR)[hat(k)+(pi+1)hat(i)]` `(c)` Magnetic field due to segment AB, `vec(B_(1))=(mu_(0)I)/(4piR)(-hat(k))` Magneticfield due to circular segment BCDE, `vec(B_(2))=(mu_(0)I)/(2R)xx((3pi//2)/(2pi))(-hat(i))` Magnetic field due to segment EF, `vec(B_(3))=(mu_(0)I)/(4piR)xx(-hat(j))` Resultant magnetic field. `vec(B_(R))=vec(B_(1))+vec(B_(2))+vec(B_(3))=-(mu_(0)I)/(4piR)[hat(k)+hat(j)+(3pi)/(2)hat(i)]` |
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