Write the formula for the magnetic field due to a circular current-carrying loop having $N$ turns and $R$ radius at a point on the axis of the loop at a distance $x$ from the center.
(N/A) The magnetic field $B$ at a point on the axis of a circular current-carrying loop is given by the Biot-Savart Law.
For a single loop with radius $R$,current $I$,and a point at distance $x$ from the center along the axis,the magnetic field is $B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$.
For a coil having $N$ turns,the total magnetic field is the sum of the fields produced by each turn.
Therefore,the formula is $B = \frac{\mu_0 N I R^2}{2(R^2 + x^2)^{3/2}}$,where $\mu_0$ is the permeability of free space.
For a single loop with radius $R$,current $I$,and a point at distance $x$ from the center along the axis,the magnetic field is $B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$.
For a coil having $N$ turns,the total magnetic field is the sum of the fields produced by each turn.
Therefore,the formula is $B = \frac{\mu_0 N I R^2}{2(R^2 + x^2)^{3/2}}$,where $\mu_0$ is the permeability of free space.
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As shown in the figure,two infinitely long straight parallel wires $P$ and $Q$ carrying equal currents in opposite directions are arranged parallel to the $Y$-axis. If the magnetic field due to wire $P$ at the origin '$O$' of the coordinate system is $B$,then match the resultant magnetic fields at various points given in Column $A$ with the points given in Column $B$. Column $A$ Column $B$ $A) \frac{B}{4}$ $i) (0, 0)$ $B) \frac{B}{2}$ $ii) (a, 0)$ $C) \frac{2B}{3}$ $iii) (2a, 0)$ $D) 2B$ $iv) (3a, 0)$
| Column $A$ | Column $B$ |
| $A) \frac{B}{4}$ | $i) (0, 0)$ |
| $B) \frac{B}{2}$ | $ii) (a, 0)$ |
| $C) \frac{2B}{3}$ | $iii) (2a, 0)$ |
| $D) 2B$ | $iv) (3a, 0)$ |
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