$A$ current $i$ ampere flows along the inner conductor of a coaxial cable and returns along the outer conductor of the cable. The magnetic induction at any point outside the conductor at a distance $r$ metre from the axis is

  • A
    $\infty$
  • B
    Zero
  • C
    $\frac{\mu_0}{4\pi} \frac{2i}{r}$
  • D
    $\frac{\mu_0}{4\pi} \frac{2\pi i}{r}$

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$A$ closely wound solenoid $120 \ cm$ long has $4$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8 \ cm$. If the current carried is $8.0 \ A$,estimate the magnitude of $B$ inside the solenoid near its centre.

$A$ solenoid is $1.5 \, m$ long and its inner diameter is $4.0 \, cm$. It has three layers of windings of $1000$ turns each and carries a current of $2.0 \, A$. The magnetic flux for a cross-section of the solenoid is nearly:

An infinitely long hollow conducting cylinder with inner radius $R/2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field,$|\vec B |$ as a function of the radial distance $r$ from the axis is best represented by:

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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 $\oint \vec{B}_T \cdot d\vec{l}$.

Derive the expression for the magnetic field inside a long straight solenoid.

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