Magnetic Field Due to a Circular Arc at the Centre

Q.

A wire $A$, bent in the shape of an arc of a circle, carrying a current of$2A$ and having radius $2cm$ and another wire $B$, also bent in the shape of arc of a circle, carrying a current of $3A$ and having radius of $4cm$, are placed as shown in the figure. The ratio of the magnetic field due to the wires $A$ and $B$ at the common centre $O$ is:

1. $2:5$

2. $6:5$

3. $6:4$

4. $4:6$

Q. The magnetic field at the centre of the circular coil carrying current of 4A is

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

Q. Magnetic field in a region is equal to B•. A loop of resistance R and radius r is lying in the field with its plane perpendicular to the field. If the loop is turned by 180⁰, find the charge which flows through a given cross section of the loop

Q.

A wire PQRS shown in Fig. carries a current l. The radius of the circular part of the wire r. The magnetic field at the centre O of the circular part of the wire is given by

1. $\frac{1}{8}\frac{{\mu }_{0}I}{r}$

2. $\frac{1}{4}\frac{{\mu }_{0}I}{r}$

3. $\frac{3}{8}\frac{{\mu }_{0}I}{r}$

4. $\frac{1}{2}\frac{{\mu }_{0}I}{r}$

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 straight wire carrying a current of 10 A is bent into a semi-circular arc of radius $\pi$ cm as shown in Fig. What is the magnitude and direction of the magnetic field at centre 0 of the arc?

1. ${10}^{-4}$ T normal to the plane of the arc and directed into the page.

2. ${10}^{-4}$ T normal to the plane of the arc and directed outside the page.

3. $2\times {10}^{-4}$ T parallel to the plane of the arc and directed to the left.

4. $2\times {10}^{-4}$ T parallel to the plane of the arc and directed to the right.

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. The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

1. $\frac{{\pi }^2}{4\sqrt{2}}$
   
2. $\frac{{\pi }^2}{8\sqrt{2}}$
   
3. $\frac{\pi }{2\sqrt{2}}$
   
4. $\frac{\pi }{4\sqrt{2}}$

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. The radius of a current carrying coil is ${}^{\prime }{R}^{\prime }$. Then, the ratio of magnetic fields at the centre of the coil and at an axial point, which is $R\sqrt{3}$ distance away from the centre of the coil is

1. $1:1$
2. $1:2$
3. $1:4$
4. $8:1$

Q. A wire $A$, bent in the shape of an arc of a circle, carrying a current of $2\text{A}$ and having radius $2\text{cm}$ and another wire $B$, also bent in the shape of arc of a circle, carrying a current of $3\text{A}$ and having radius of $4\text{cm}$, are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is :

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

Q. The radius of a current carrying coil is ${}^{\prime }{R}^{\prime }$. Then, the ratio of magnetic fields at the centre of the coil and at an axial point, which is $R\sqrt{3}$ distance away from the centre of the coil is

1. $1:1$
2. $1:2$
3. $1:4$
4. $8:1$

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. If we double the radius of a current carrying circular arc keeping the current unchanged, the magnetic field at its center will be .

1. halved
2. quartered
3. unchanged

Q.

In the figure shown there are two semicircles of radii $r_1$ and $r_2$ in which a current i is flowing. The magnetic induction at the centre O will be

1. $\frac{{\mu }_{0}i}{r}(r_1+r_2)$

2. $\frac{{\mu }_{0}i}{4}(r_1-r_2)$

3. $\frac{{\mu }_{0}i}{4}\left(\frac{r_1+r_2}{r_1{r}_2}\right)$

4. $\frac{{\mu }_{0}i}{4}\left(\frac{r_2-r_1}{r_1{r}_2}\right)$

Q. A semicircular wire fo radius 'R' carries a current 'i'. What will be the magnetic field strength at its centre?

1. $\frac{{\mu }_{0}i}{2R}$
2. $\frac{{\mu }_{0}i}{R}$
3. $\frac{{\mu }_{0}i}{4R}$
4. $\frac{{\mu }_{0}i}{8R}$