As shown in Fig. there are two semicircles of radii r1=12 cm and r2=10 cm in which 4 Amp curre

step 1 In this problem magnetic field due to AB and DE is equal to 0. I can write B, B -C -D is equal t

As shown in Fig. there are two semicircles of radii r1=12...

As shown in Fig. there are two semicircles of radii $\mathrm{r}_{1}=12 \mathrm{~cm}$ and $r_{2}=10 \mathrm{~cm}$ in which 4 Amp current is following The mag. field at the centre ${ }^{n} \mathrm{O}^{n}$ is(a) $(55 / 3) \mu_{0}$ going inside (b) $(3 / 55) \mu_{0}$ going outside (c) $(6 / 55) \mu_{0}$ going inside (d) $(12 / 55) \mu_{0}$ going inside

As shown in Fig. there are two semicircles of radii $\mathrm{r}_{1}=12 \mathrm{~cm}$ and $r_{2}=10 \mathrm{~cm}$ in which 4 Amp current is following The mag. field at the centre ${ }^{n} \mathrm{O}^{n}$ is(a) $(55 / 3) \mu_{0}$ going inside
(b) $(3 / 55) \mu_{0}$ going outside
(c) $(6 / 55) \mu_{0}$ going inside
(d) $(12 / 55) \mu_{0}$ going inside

Key Concepts

Right?Hand Rule

The right?hand rule is a mnemonic used to determine the direction of the magnetic field generated by a current-carrying conductor. By pointing the thumb in the direction of the conventional current and curling the fingers, one obtains the field direction around the conductor. This rule is essential for deciding whether the magnetic field at a given point, due to semicircular arcs, points inward or outward relative to the loop.

Superposition Principle for Magnetic Fields

When multiple current-carrying segments contribute to the magnetic field at a point, the net magnetic field is found by vectorially adding the individual fields. This principle is crucial when dealing with configurations that include multiple semicircular arcs, as their fields need to be combined to obtain the total field at the center.

Biot?Savart Law

This law provides the fundamental method to compute the magnetic field produced by a small segment of current-carrying wire. It expresses the differential magnetic field contribution from an element of current in terms of the current magnitude, the length element, the distance from the element to the point of interest, and the sine of the angle between the element and the line connecting it to the point. The law is central to calculating the magnetic field for arbitrarily shaped current paths.

Magnetic Field of a Circular Arc

For a circular arc carrying a current, the magnetic field at the center can be calculated using an integration of the Biot?Savart law over the extent of the arc. The field is proportional to the current and the subtended angle of the arc and inversely proportional to the radius. This principle simplifies the analysis of semicircular wires by providing a direct formula for the contribution of an arc to the magnetic field at its center.

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