IGNOU BPHCT 133 2026 - Using Biot-Savart's law, obtain an expression for the magnetic fie

Question

Using Biot-Savart's law, obtain an expression for the magnetic field due to electric current flowing in a long straight wire at a distance R from the wire along a line perpendicular to the wire.

19 Jan 2026

Answer :

Word Count : 459

The Biot-Savart law provides a fundamental relationship to calculate the magnetic field produced by a steady current. According to this law, the infinitesimal contribution (d\mathbf{B}) to the magnetic field at a point in space due to an element of current-carrying conductor is given by [ d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I , d\mathbf{l} \times \mathbf{\hat{r}}}{r^2} ] where (I) is the current in the conductor, (d\mathbf{l}) is an infinitesimal element of the wire in the direction of current, (\mathbf{r}) is the position vector from the element to the observation point, (r = |\mathbf{r}|), and (\mathbf{\hat{r}} = \mathbf{r}/r) is the unit vector along (\mathbf{r}). (\mu_0) is the permeability of free space, having the value (4\pi \times 10^{-7},\text{T·m/A}). Consider a long straight wire carrying

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