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(D) The magnetic field $B$ at the centre of a circular arc subtending an angle $	heta$ at the centre is given by $B = \frac{	heta}{2 \pi} 	imes \fr

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$\frac{3 \mu_0 I}{8 R}$ in upward direction

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(D) The magnetic field $B$ at the centre of a circular arc subtending an angle $	heta$ at the centre is given by $B = \frac{	heta}{2 \pi} 	imes \frac{\mu_0 I}{2 R}$.Here,the arc is $\frac{3}{4}$ of the circumference,so the angle subtended is $	heta = \frac{3}{4} 	imes 2 \pi = \frac{3 \pi}{2} 	ext{ radians}$.Substituting the value of $	heta$ into the formula:$B = \frac{3 \pi / 2}{2 \pi} 	imes \frac{\mu_0 I}{2 R} = \frac{3}{4} 	imes \frac{\mu_0 I}{2 R} = \frac{3 \mu_0 I}{8 R}$.According to the right-hand thumb rule,since the current flows in an anticlockwise direction,the magnetic field at the centre will be directed upwards.

$A$ current $I$ flows in an anticlockwise direction in a circular arc of a wire having $\left(\frac{3}{4}\right)^{\text{th}}$ of the circumference of a circle of radius $R$. The magnetic field $B$ at the centre of the circle is $(\mu_0 = \text{permeability of free space})$

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