A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the $X-Y$ plane and a steady current ' $I$ ' flows through the wire. The $Z$-component of the magnetic field at the center of the spiral is
A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the $X-Y$ plane and a steady current ' $I$ ' flows through the wire. The $Z$-component of the magnetic field at the center of the spiral is
- [IIT 2011]
- A
$\frac{\mu_0 N I}{2(b-a)} \ln \left(\frac{b}{a}\right)$
- B
$\frac{\mu_0 N I}{2(b-a)} \ln \left(\frac{b+a}{b-a}\right)$
- C
$\frac{\mu_0 N I}{2 b} \ln \left(\frac{b}{a}\right)$
- D
$\frac{\mu_0 N I}{2 b} \ln \left(\frac{b+a}{b-a}\right)$
Similar Questions
Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field by both coils, if the same current is flown
Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field by both coils, if the same current is flown
Two concentric coils each of radius equal to $2\pi \,{\rm{ }}cm$ are placed at right angles to each other. $3$ $ampere$ and $4$ $ampere$ are the currents flowing in each coil respectively. The magnetic induction in $Weber/{m^2}$ at the centre of the coils will be $({\mu _0} = 4\pi \times {10^{ - 7}}\,Wb/A.m)$
Two concentric coils each of radius equal to $2\pi \,{\rm{ }}cm$ are placed at right angles to each other. $3$ $ampere$ and $4$ $ampere$ are the currents flowing in each coil respectively. The magnetic induction in $Weber/{m^2}$ at the centre of the coils will be $({\mu _0} = 4\pi \times {10^{ - 7}}\,Wb/A.m)$
- [AIIMS 2008]
The magnetic induction at the centre $O$ in the figure shown is
The magnetic induction at the centre $O$ in the figure shown is
- [IIT 1988]
If induction of magnetic field at a point is $B$ and energy density is $U$ then which of the following graphs is correct
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A current $I$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $R$. The magnitude of the magnetic induction along its axis is:
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- [AIEEE 2011]