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A small circular loop of radius a is pla...

A small circular loop of radius a is placed inside a large square loop of edge `L(gt gta)` . The loops are coplanar and concentric. Find mutual inductance.

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To find the mutual inductance between a small circular loop of radius \( a \) and a large square loop of edge \( L \) (where \( L > a \)), we can follow these steps: ### Step 1: Understand the Configuration We have a small circular loop of radius \( a \) placed inside a large square loop with edge length \( L \). Both loops are coplanar and concentric. ### Step 2: Determine the Magnetic Field Due to the Square Loop The magnetic field \( B \) at the center of the square loop due to the current \( I \) flowing through it can be calculated. The magnetic field at the center of a square loop can be derived using the formula: ...
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A small square loop of wire of side l is placed inside a large squre loop of wire of side L (gt gt l) . The loops are coplanar and their centre coincide. What is the mutual inductance of the system ?

A small square loop of wire of side l is placed inside a large square loop of wire of side (L gt gt l) . The loops are coplanar and their centres coincide. If the mutual inductance of the system is p sqrt(q) (mu_(0))/(pi) (l^(2))/(L) , then find (p+q) .

Knowledge Check

  • A small square loop of wire of side l is placed inside a large square loop of wire of side L(Lgtgtl) . The loops are co-planer and their centres coincide. The mutual inductance of the system is proportional to

    A
    `l/L`
    B
    `l^(2)/L`
    C
    `L/l`
    D
    `L^(2)/l`

  • A very small circular loop of radius a is initially coplanar & concentric with a much larger circular loop of radius b (gtgta) . A constant current is passed in the large loop which is kept fixed in space & the small loop is rotated with angular velocity omega about a diameter. The resistance of the small loop is R & its self inductance is negligible. The current in the larger loop is clockwise. Find the current in the small loop as a function of time.

    A
    `(pia^(2)mu_(0)Iomegasinomegat)/(2bR)`
    B
    `(pia^(2)mu_(0)Iomegacosomegat)/(2bR)`
    C
    `(pib^(2)mu_(0)Iomegasinomegat)/(2aR)`
    D
    `(pib^(2)mu_(0)Iomegacosomegat)/(2aR)`

  • A very small circular loop of radius a is initially coplanar & concentric with a much larger circular loop of radius b (gtgta) . A constant current is passed in the large loop which is kept fixed in space & the small loop is rotated with angular velocity omega about a diameter. The resistance of the small loop is R & its self inductance is negligible. The current in the larger loop is clockwise. Calculate how much torque must be exerted on the small loop to rotate it.

    A
    `omega/R((pib^(2)mu_(0)Isinomegat)/(2b))^(2)`
    B
    `omega/R((pib^(2)mu_(0)I)/(2b))^(2)sinomegatcosomegat`
    C
    `omega/R((pia^(2)mu_(0)Isinomegat)/(2b))^(2)`
    D
    None of these

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