Magnetic Field Due to a Circular Arc at the Centre

Q. A thin conducting ring of radius $R$ is given a charge $+Q$ uniformly distributed over its circumference. The electric field at the centre $O$ of the ring due to the charge on the part $\text{AKB}$ of the ring is $E$. The electric field at the centre due to the charge on the part $\text{ACDB}$ of the ring is

1. $3E$ along $\text{KO}$
2. $E$ along $\text{OK}$
3. $E$ along $\text{KO}$
4. $3E$ along $\text{OK}$

Q.

A circular wire loop of radius a carries a total charge Q distributed uniformly over its length. A small length DL of the wire is cut off. Find the electric field at the centre due to the remaining wire.

Q.

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on its axis at a distance of 4 cm from the centre is 54 $\mu$T. The magnetic field (in $\mu$T) at the centre of the loop will be

1. 250

2. 150

3. 125

4. 72

Q. Radius of current carrying coil is ${}^{\prime }{R}^{\prime }$. Then ratio of magnetic fields at the centre of the coil to the 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 uniformly charged ring with radius $0.5\text{m}$ has $0.002\pi \text{m}$ gap. If the ring carries a charge of $+1\text{C}$, the electric field at the centre is

1. $7.5\times {10}^7{\text{NC}}^{-1}$
2. $7.2\times {10}^7{\text{NC}}^{-1}$
3. $6.2\times {10}^7{\text{NC}}^{-1}$
4. $6.5\times {10}^7{\text{NC}}^{-1}$

Q. For the given semi-infinite rod of uniformly distributed line charge, find the net electric field at point $\text{P}$.

1. $3.4\times {10}^5\text{N/C}$
2. $4.4\times {10}^5\text{N/C}$
3. $5.4\times {10}^5\text{N/C}$
4. $6.4\times {10}^5\text{N/C}$

Q. A bar magnet of length $l$ and magnetic dipole moment $M$ is bent to form an arc which subtends an angle of ${120}^{\circ }$ at centre. The new magnetic dipole moment will be

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

Q. The magnetic field at the center of current carrying circular loop is $B_1$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_2$. The value of $B_1/B_2$ will

1. $5:\sqrt{3}$
2. $8:1$
3. $12:\sqrt{5}$
4. $9:4$

Q. A wire of length l carries a current i along the X-axis. A magnetic field exists which is given as $B=B_0(\hat{i}+\hat{j}+\hat{k})$ T. Find the magnitude of the magnetic force acting on the wire

1. $\frac{1}{\sqrt{2}}\times B_{0}il$
2. $B_{0}il$
   
3. $B_{0}il\times \sqrt{2}$
   
4. $2B_{0}il$
   

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

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. 
2. 
3. 
4. 

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

Q.

Two concentric coils each of radius equal to 2 $\pi$ cm are placed right angles to each other. If 3A and 4A are the currents flowing through the two coils respectively. The magnetic induction (in Wb m-2) at the center of the coils will be

1. $5\times {10}^{-5}$

2. $12\times {10}^{-5}$

3. $7\times {10}^{-5}$

4. ${10}^{-5}$

Q.

State Biot – Savart law. Deduce the expression for the magnetic field at a point on the axis of a current carrying circular loop of radius ‘R’ at a distance ‘x’ from the centre. Hence, write the magnetic field at the centre of a loop.

Q. The magnetic moment $\left(\mu \right)$ of an electron revolving around the nucleus, varies with principal quantum number $n$ as,

1. $\mu \propto n$
2. $\mu \propto \frac{1}{n}$
3. $\mu \propto n^2$
4. $\mu \propto \frac{1}{n^2}$

Q.

A part of a long wire carrying a current I is bent into a circle of radius r as shown in Fig. The net magnetic field at the centre O of the corcular loop is

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

2. $\frac{{\mu }_{0}I}{2\pi r}(\pi +1)$

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

4. $\frac{{\mu }_{0}I}{2\pi r}(\pi -1)$

Q. The radius of a coil of wire with $N$ turns is $0.22\text{m}$ and $3.5\text{A}$ current flows clockwise in the coil as shown. A long straight wire carrying a current $54\text{A}$ towards the left is located $0.05$ meters from the edge of the coil. The magnetic field at the centre of the coil is zero tesla. The number of turns $N$ in the coil are:

Q. Due to the flow of current in a circular loop of radius $R$, the magnetic field produced at the centre of the loop is $B$. The magnetic moment of the loop is:-

1. $\frac{B{R}^2}{2\pi {\mu }_0}$
2. $\frac{2\pi B{R}^3}{{\mu }_0}$
3. $\frac{B{R}^2}{2\pi {\mu }_0}$
4. $\frac{2\pi B{R}^2}{{\mu }_0}$

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 outside the page.

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

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

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

Q.

Do AC motors have slip rings?

Q.

Two concentric coils X and Y of radii 16 cm and 10 cm lie in the same vertical plane containing N-S direction. X has 20 turns and carries 16 A. Y has 25 turns and carries 18 A. X has current in anticlockwise direction and Y has current in clockwise direction for an observer, looking at the coils facing the west. The magnitude of net magnetic field at their common centre is

1. $5\pi \times {10}^{-4}T$ towards west

2. $13\pi \times {10}^{-4}T$ towards east

3. $13\pi \times {10}^{-4}T$ towards west

4. $5\pi \times {10}^{-4}T$ towards east

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

Q.

What is magnetic intensity and magnetizing (magnetic ) field?

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

Q.

The radius of a circular current-carrying coil is $R$. At what distance from the center of the coil on its axis, the intensity of the magnetic field will be $\frac{1}{2\sqrt{2}}$ times at the center?

Q. Three rings, each having equal radius $R$, are placed mutually perpendicular to each other and each having its centre at the origin of co-ordinate system. If current $I$ is flowing through each ring then the magnitude of the magnetic field at the common centre is

1. $\sqrt{3}\frac{{\mu }_{0}I}{2R}$
2. zero
3. $(\sqrt{2}-1)\frac{{\mu }_{0}I}{2R}$
4. $(\sqrt{3}-\sqrt{2})\frac{{\mu }_{0}I}{2R}$

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

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. $6.3\times {10}^{-4}Tesla$

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

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

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

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