A current I flows through a closed loop made of two straight radial segments (which pass through the centre O and so contribute no field there) joined by two circular arcs of radius R, as shown in a typical textbook figure where the arcs subtend an angle 2θ and (2π-2θ) respectively at O. What is the magnitude of the magnetic field at the centre O?

PhysicsMediumHigh School (11–12)jee-main

For a circular arc of radius $R$ carrying current $I$ and subtending angle $\phi$ at the centre, the field at the centre is $B=\dfrac{\mu_0 I \phi}{4\pi R}$ . Straight segments that lie along a line passing through the observation point produce zero magnetic field there, since $d\mathbf{l}\times\hat{r}=0$ .

A current $I$ flows through a closed loop made of two straight radial segments (which pass through the centre $O$ and so contribute no field there) joined by two circular arcs of radius $R$ , as shown in a typical textbook figure where the arcs subtend an angle $2\theta$ and $(2\pi-2\theta)$ respectively at $O$ . What is the magnitude of the magnetic field at the centre $O$ ?

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← Consider the following two statements about the magnetic (Lorentz) force on a moving charge: Statement I: The magnetic force experienced by a moving charged particle in a magnetic field is invariant in nature, just like any other force (e.g., gravity or a spring force). Statement II: The magnetic force on a charged particle is given by F=q(v×B), where v is the velocity of the particle measured with respect to the frame of reference in which F is being calculated. Which of the following is correct?A current-carrying loop lies in the xy-plane, shaped as shown in a standard textbook figure: it consists of a square loop of side a with two semicircular lobes of radius a attached on opposite sides, with current I flowing around the loop in a sense such that the unit vector k̂ (out of the page) gives the direction of the magnetic moment. What is the magnetic moment of this current loop? →

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