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Assertion At the centre of a circular c...

Assertion At the centre of a circular current carrying loop `(I_(1))`, there is an infinitely long straight of the circle. Then magnetic force of attraction between two is zero.
Reason Magnetic field of `I_(1)` at centre is inwards, parallel to `I_(2)`.

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To solve the problem, we need to analyze the assertion and reason provided in the question regarding the magnetic field and forces between a circular current-carrying loop and an infinitely long straight wire. ### Step-by-Step Solution: 1. **Understanding the Setup**: - We have a circular loop carrying a current \( I_1 \) and an infinitely long straight wire carrying a current \( I_2 \) placed at the center of the loop. 2. **Magnetic Field at the Center of the Loop**: - The magnetic field \( B \) at the center of a circular loop carrying current \( I_1 \) can be determined using the right-hand rule. If the current flows in a clockwise direction, the magnetic field at the center will point downwards (into the plane). If it flows counterclockwise, the magnetic field will point upwards (out of the plane). 3. **Direction of the Magnetic Field**: - According to the assertion, the magnetic field at the center of the loop is directed inward (which corresponds to a clockwise current). This is consistent with the right-hand rule, where curling the fingers in the direction of the current gives the direction of the magnetic field. 4. **Force on the Straight Wire**: - The magnetic force \( F \) on a current-carrying conductor in a magnetic field is given by the formula: \[ F = I L \times B \] - Here, \( I \) is the current in the wire, \( L \) is the length of the wire segment in the magnetic field, and \( B \) is the magnetic field strength. The direction of the force is determined by the angle \( \theta \) between the current direction in the wire and the magnetic field direction. 5. **Angle Between Current and Magnetic Field**: - If the current \( I_2 \) in the straight wire is parallel to the magnetic field \( B \) (both pointing in the same direction) or anti-parallel (pointing in opposite directions), the angle \( \theta \) is either \( 0^\circ \) or \( 180^\circ \). - In both cases, \( \sin \theta = 0 \), leading to: \[ F = I_2 L B \sin \theta = 0 \] - Therefore, the magnetic force of attraction between the loop and the straight wire is zero. 6. **Conclusion**: - The assertion is true: the magnetic force of attraction between the circular loop and the straight wire is zero. - The reason is also true: the magnetic field at the center of the loop is inward and parallel to the current in the wire. ### Final Answer: Both the assertion and the reason are true, and the reason correctly explains the assertion. ---
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