(B) The magnetic field $B$ inside a toroidal solenoid is given by $B = \frac{\mu_{0} N I}{2 \pi R}$.The magnetic flux $\phi$ through each turn is $\ph

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$\frac{\mu_{0} N^{2} A}{2 \pi R}$

(B) The magnetic field $B$ inside a toroidal solenoid is given by $B = \frac{\mu_{0} N I}{2 \pi R}$.The magnetic flux $\phi$ through each turn is $\phi = B \cdot A = \frac{\mu_{0} N I A}{2 \pi R}$.The total flux linkage is $N \phi = \frac{\mu_{0} N^{2} I A}{2 \pi R}$.By definition,the self-inductance $L$ is given by $L = \frac{N \phi}{I}$.Substituting the expression for total flux linkage,we get $L = \frac{\mu_{0} N^{2} A}{2 \pi R}$.

Class 12 Physics Moving Charges and Magnetism Ampere’s circuital law and its application (Solenoid and Toroid)

Easy

$A$ toroidal solenoid with air core has an average radius $R$,number of turns $N$,and area of cross-section $A$. The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid).

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A
$\frac{\mu_{0} N^{2} A}{R}$
B
$\frac{\mu_{0} N^{2} A}{2 \pi R}$
C
$\frac{\mu_{0} NA}{2 \pi R}$
D
$\frac{\mu_{0} NA}{R}$

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Class 12

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Chapter

Moving Charges and Magnetism

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Ampere’s circuital law and its application (Solenoid and Toroid)

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$A$ toroid has a core (non-ferromagnetic) of inner radius $25 \; cm$ and outer radius $26 \; cm,$ around which $3500$ turns of a wire are wound. If the current in the wire is $11 \; A$,what is the magnetic field:
$(a)$ outside the toroid,
$(b)$ inside the core of the toroid,and
$(c)$ in the empty space surrounded by the toroid?

Medium

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In the following diagram,there is a straight wire carrying a current $I$. Consider a circular path with radius $R$ near it. If $\vec{B}_T$ is the tangential component of the magnetic field along the circular path,then find the value of the integral $\oint \vec{B}_T \cdot d\vec{l}$.

Medium

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$A$ long solenoid has $200$ turns per cm and carries a current of $2.5 \, A$. The magnetic field at its centre is (given $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m/A$):

Easy

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$A$ coil wrapped around a toroid has an inner radius of $20 \,cm$ and an outer radius of $25 \,cm$. If the wire wrapping makes $800$ turns and carries a current of $12 \,A$, the maximum and minimum values of the magnetic field within the toroid are:

MediumAP EAMCET 2021

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$A$ solenoid has a turn density of $5000 \, \text{turns/m}$ and a cross-sectional area of $10 \, \text{cm}^2$. If a current of $1 \, \text{A}$ flows through it and the core material has a relative permeability of $1000$, find the energy per unit length of the solenoid in $\text{J/m}$.

Medium

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$A$ toroidal solenoid with air core has an average radius $R$,number of turns $N$,and area of cross-section $A$. The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid).

Similar Questions

In the following diagram,there is a straight wire carrying a current $I$. Consider a circular path with radius $R$ near it. If $\vec{B}_T$ is the tangential component of the magnetic field along the circular path,then find the value of the integral $\oint \vec{B}_T \cdot d\vec{l}$.

$A$ long solenoid has $200$ turns per cm and carries a current of $2.5 \, A$. The magnetic field at its centre is (given $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m/A$):

$A$ coil wrapped around a toroid has an inner radius of $20 \,cm$ and an outer radius of $25 \,cm$. If the wire wrapping makes $800$ turns and carries a current of $12 \,A$, the maximum and minimum values of the magnetic field within the toroid are:

$A$ solenoid has a turn density of $5000 \, \text{turns/m}$ and a cross-sectional area of $10 \, \text{cm}^2$. If a current of $1 \, \text{A}$ flows through it and the core material has a relative permeability of $1000$, find the energy per unit length of the solenoid in $\text{J/m}$.

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