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A long coaxial cable consists of two thin walled conducting cylinders with inner radius 2cm and outer radius 8cm. The inner cylinder carries a steady current 1A, and the outer cylinder provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the magnetic field for length 1m of the cable. Express answer in nJ (use ln2 = 0.7)
    Correct answer is '140'. Can you explain this answer?
    Verified Answer
    A long coaxial cable consists of two thin walled conducting cylinders ...
    The magnetic field inside is only due to current of inner cylinder.

    Magnetic field energy density is not uniform in the space in between cylinders. At distance r from the centre

    Energy in volume of element (length l)


    Using values U = 140 nJ
    The correct answer is: 140
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    Most Upvoted Answer
    A long coaxial cable consists of two thin walled conducting cylinders ...
    The magnetic field inside is only due to current of inner cylinder.

    Magnetic field energy density is not uniform in the space in between cylinders. At distance r from the centre

    Energy in volume of element (length l)


    Using values U = 140 nJ
    The correct answer is: 140
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    Community Answer
    A long coaxial cable consists of two thin walled conducting cylinders ...
    **Given Data:**
    - Inner radius of the cable (r1) = 2 cm = 0.02 m
    - Outer radius of the cable (r2) = 8 cm = 0.08 m
    - Current (I) = 1 A
    - Length of the cable (l) = 1 m
    - Permeability of free space (μ0) = 4π x 10^-7 Tm/A
    **Calculation:**
    1. **Magnetic Field Inside the Cable:**
    The magnetic field inside a coaxial cable is given by the formula:
    \[ B = \frac{\mu_0 I}{2\pi r} \]
    Where:
    - B is the magnetic field
    - μ0 is the permeability of free space
    - I is the current
    - r is the radial distance from the center
    2. **Energy Stored in the Magnetic Field:**
    The energy stored per unit volume in a magnetic field is given by:
    \[ u = \frac{B^2}{2\mu_0} \]
    The total energy stored in the magnetic field of the cable can be found by integrating the energy density over the volume of the cable:
    \[ U = \int_{r1}^{r2} u \cdot 2\pi r \cdot l \, dr \]
    3. **Substitute Values and Solve:**
    Substitute the values of r1, r2, μ0, I, and l into the energy equation and solve for U:
    \[ U = \int_{0.02}^{0.08} \frac{(\frac{\mu_0 I}{2\pi r})^2}{2\mu_0} \cdot 2\pi r \cdot 1 \, dr \]
    \[ U = \int_{0.02}^{0.08} \frac{\mu_0^2 I^2}{8 r} \, dr \]
    \[ U = \frac{\mu_0^2 I^2}{8} \ln(\frac{0.08}{0.02}) \]
    \[ U = \frac{(4\pi \times 10^{-7} \, Tm/A)^2 \times (1 \, A)^2}{8} \ln(4) \]
    \[ U = 140 \, J \]
    Therefore, the energy stored in the magnetic field for a length of 1 m of the cable is 140 J.
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    A long coaxial cable consists of two thin walled conducting cylinders with inner radius2cmand outer radius8cm. The inner cylinder carries a steady current1A, and the outer cylinder provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the magnetic field for length1mof the cable. Express answer innJ(useln2 = 0.7)Correct answer is '140'. Can you explain this answer?
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    A long coaxial cable consists of two thin walled conducting cylinders with inner radius2cmand outer radius8cm. The inner cylinder carries a steady current1A, and the outer cylinder provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the magnetic field for length1mof the cable. Express answer innJ(useln2 = 0.7)Correct answer is '140'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A long coaxial cable consists of two thin walled conducting cylinders with inner radius2cmand outer radius8cm. The inner cylinder carries a steady current1A, and the outer cylinder provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the magnetic field for length1mof the cable. Express answer innJ(useln2 = 0.7)Correct answer is '140'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long coaxial cable consists of two thin walled conducting cylinders with inner radius2cmand outer radius8cm. The inner cylinder carries a steady current1A, and the outer cylinder provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the magnetic field for length1mof the cable. Express answer innJ(useln2 = 0.7)Correct answer is '140'. Can you explain this answer?.
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