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QPages 230-234: Q13: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q13 Solution: A hypothetical magnetic field existing in a region is given by…

A hypothetical magnetic field existing in a region is given by B⃗=B0e^r\vec{B} = B_0 \hat{e}_r where e^r\hat{e}_r denotes the unit vector along the radial direction. A circular loop of radius aa, carrying a current ii, is placed with its plane parallel to the x−yx - y plane and the centre at 0, 0, dd). Find the magnitude of the magnetic force acting on the loop.

Step-by-Step Verified Solution

**Answer:** F=2πaiB0F = 2\pi a i B_0. **Step-by-Step Explanation:** Given: B⃗=B0e^r\vec{B} = B_0 \hat{e}_r. The force on each element dF⃗=idl⃗×B⃗d\vec{F} = i d\vec{l} \times \vec{B}. Since dl⃗d\vec{l} is tangential and B⃗\vec{B} is radial, the force is vertical (along z-axis). The net force is F=2πaiB0F = 2\pi a i B_0.

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