$6$(a) (i) A rectangular loop of sides a and b carrying current I is placed in a magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$ such that its area vector $\displaystyle \overrightarrow{\mathrm{A}}$ makes an angle $\displaystyle \theta$ with $\displaystyle \overrightarrow{\mathrm{B}}$. With the help of a suitable diagram, show that the torque $\displaystyle \vec{\tau}$ acting on the loop is given by $\displaystyle \vec{\tau}=\vec{\mathrm{m}} \times \vec{\mathrm{B}}$, where $\displaystyle \vec{\mathrm{m}}(=\mathrm{I} \vec{\mathrm{A}})$ is the magnetic dipole moment of the loop. (ii) A circular coil of 100 turns and radius $\displaystyle \left(\frac{10}{\sqrt{\pi}}\right) \mathrm{cm}$ carrying current of $\displaystyle 5 \cdot 0 \mathrm{~A}$ is suspended vertically in a uniform horizontal magnetic field of 2.0 T. The field makes an angle 30° with the normal to the coil. Calculate : (I) the magnetic dipole moment of the coil, and (II) the magnitude of the counter torque that must be applied to prevent the coil from turning.

OR

(b) (i) Derive an expression for the force $\displaystyle \overrightarrow{\mathrm{F}}$ acting on a conductor of length L and area of cross-section A carrying current I and placed in a magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$. (ii) A part of a wire carrying 2.0 A current and bent at 90° at two points is placed in a region of uniform magnetic field $\displaystyle \overrightarrow{\mathrm{B}}=-(0.50 \mathrm{~T}) \hat{\mathrm{k}}$, as shown in the figure. Calculate the magnitude of the net force acting on the wire. 2026_CBSE_Physics_Set_Region5_Subset_Set1_Q32__ii_p15_28

2026_CBSE_Physics_Set_Region5_Subset_Set1_Q32__ii_p15_28

Physics · Moving Charges and Magnetism · Torque on Current Loop, Magnetic Dipole