Magnetic Field Due to a Circular Arc at the Centre

Q. A current I flows in circular arc of wire which subtends an angle ${\theta }^{\circ }$ at the centre. If the radius of the circle is r then the magnetic field B at center is:

1. $\frac{{\mu }_{0}i}{r}$
2. $\frac{{\mu }_{0}i}{2r}$
3. $\frac{3{\mu }_{0}i}{4r}$
4. $\frac{\left(\frac{{\theta }^{\circ }}{{360}^{\circ }}\right){\mu }_{0}i}{2r}$

Q.

A long cylindrical conductor of radius 'a' has two cylindrical cavities each of diameter 'a' through its entire length as shown in the figure. A current I is directed out of the page and is uniform throughout the cross-section of the conductor. The magnetic field at point $P_1$ is

1. $\frac{{\mu }_{0}I}{2\pi r}\left(\frac{2r^2+a^2}{4r^2-a^2}\right)$ to the right

2. $\frac{{\mu }_{0}I}{2\pi }\left(\frac{r^2+a^2}{r^2-a^2}\right)$ to the right

3. $\frac{{\mu }_{0}I}{\pi r}\left(\frac{2r^2+a^2}{2r^2-a^2}\right)$ to the left

4. $\frac{{\mu }_{0}I}{2\pi r}\left(\frac{2r^2-a^2}{4r^2-a^2}\right)$ to the left

Q. A wire is bent into the form of semicircle of radius R and carry current i. Magnetic field at point P as shown in figure is $B=\frac{{\mu }_{0}i}{a\pi R}ln(b+c)$

1. $a=5$
2. $b=\sqrt{2}$
3. $C=0$
4. $a+c=5$

Q. Find $B_0$

1. $\frac{{\mu }_{0}i}{2}[\frac{1}{a}+\frac{1}{b}]$
2. $\frac{{\mu }_{0}i}{4}[\frac{1}{a}-\frac{1}{b}]$
3. $Zero$
4. $\frac{{\mu }_{0}i}{4}[\frac{1}{a}+\frac{1}{b}]$

Q. A pizza shaped wire carries a current of 5A as shown below. If the angle subtended is $\frac{\pi }{3}$ radians and its radius is 10 cm, what will be the strength of magnetic field due to it at its centre? (Magnetic field due to straight wire at any point passing through it will be zero)

1. $\frac{{\mu }_{0}i}{6R}$
2. $\frac{{\mu }_{0}i}{12R}$
3. $\frac{{\mu }_{0}i}{3R}$
4. $\frac{{\mu }_{0}i}{18R}$

Q. A cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $={60}^{\circ }$. If $B_1$ and $B_2$ are the magnitudes of the magnetic fields at O due to the currents in $ABC$ and ADC respectively, the ratio $\frac{B_1}{B_2}$ is

1. $0.2$
2. $6$
3. $1$
4. $5$

Q. A current of $0.1\text{A}$ circulates around a coil of $100$ turns and having a radius equal to $5\text{cm}$. The magnetic field set up at the centre of the coil is
(${\mu }_0=4\pi \times {10}^{-7}\text{weber/ampere-metre}$)

1. $4\pi \times {10}^{-5}\text{tesla}$
2. $8\pi \times {10}^{-5}\text{tesla}$
3. $4\times {10}^{-5}\text{tesla}$
4. $2\times {10}^{-5}\text{tesla}$

Q. The ratio of magnitude of magnetic field at the centre of a circular current carrying coil to its magnetic moment is N. If the current and radius both were doubled the ratio will become

1. $\frac{N}{8}$
2. $\frac{N}{4}$
3. 2N
4. 4 N

Q. A 50 turn closely wound circular coil of radius 12 cm carries a current of 2.4 A, the field at center of coil is.

1. $6.3\times {10}^{-3}Tesla$
2. $4.8\times {10}^{-4}Tesla$
3. $2.4\times {10}^{-4}Tesla$
4. $6.3\times {10}^{-4}Tesla$