Definition of Ampere

Q. A wire having a semi circular loop of radius $r$ carries a current $i$ as shown in figure. The magnetic field at the center $\text{C}$ due to entire wire is

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

Q. Find the magnetic field $B$ at the center of square loop of side $a$ carrying a current $I$.

1. $\frac{{\mu }_0}{4\pi }\frac{I}{a}$
2. $\frac{{\mu }_0}{4\pi }\frac{I}{a}8\sqrt{2}$
3. $\frac{{\mu }_0}{4}\frac{I}{a}$
4. $\frac{{\mu }_0}{2\pi }\frac{I}{a}$

Q. Two identical long conducting wires $AOB$ and $COD$ are placed at right angle to each other, with one above other such that ${}^{\prime }{O}^{\prime }$ their common point for the two. The wires carry $I_1\text{and}{I}_2$ currents respectively. Point ${}^{\prime }{P}^{\prime }$ is lying at distance ${}^{\prime }{d}^{\prime }$ from ${}^{\prime }{O}^{\prime }$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point ${}^{\prime }{P}^{\prime }$ will be

1. $\frac{{\mu }_0}{2\pi d}\left(\frac{I_1}{I_2}\right)$
2. $\frac{{\mu }_0}{2\pi d}(I_1+I_2)$
3. $\frac{{\mu }_0}{2\pi d}(I_1^2-I_2^2)$
4. $\frac{{\mu }_0}{2\pi d}(I_1^2+I_2^2{)}^{\frac{1}{2}}$

Q. An element $\Delta l=\Delta x\hat{i}$ is placed at the origin and carries a large current $I=10\text{A}$, The magnetic field on the $y-\text{axis}$ at a distance of $0.5\text{m}$ is
$[\text{Take,}\Delta x=1\text{cm}]$

1. $\overrightarrow{dB}=4\times {10}^{-8}\text{T}\hat{k}$
2. $\overrightarrow{dB}=2\times {10}^{-8}\text{T}\hat{k}$
3. $\overrightarrow{dB}=1\times {10}^{-8}\text{T}\hat{k}$
4. $\overrightarrow{dB}=16\times {10}^{-8}\text{T}\hat{k}$

Q. A charge of 1 $\text{coulomb}$ is placed at one end of a non-conducting rod of length $0.6\text{m}$. Half of the charge is removed from one end and placed on the other end. The rod is rotated in a vertical plane about a horizontal axis passing through the mid-point of the rod with angular frequency ${10}^4\pi \text{rad/s}$. The magnetic field at a point on the axis at a distance of $0.4\text{m}$ from centre of rod will be :

1. $1.3\times {10}^{-3}\text{T}$
2. $2.26\times {10}^{-3}\text{T}$
3. $2.75\times {10}^{-3}\text{T}$
4. $3.8\times {10}^{-3}\text{T}$

Q. Find the magnitude and direction of magnetic field at point $P$ due to the current carrying wire as shown in figure below.

1. -$\frac{{\mu }_{0}I}{4\pi a}[-\frac{\sqrt{3}}{2}+\frac{1}{2}]$
2. $\frac{{\mu }_{0}I}{2\pi a}[\frac{\sqrt{3}}{2}-\frac{1}{2}]$
3. $\frac{{\mu }_{0}I}{4\pi a}[\frac{\sqrt{3}}{2}-\frac{1}{2}]$
4. -$\frac{{\mu }_{0}I}{2\pi a}[-\frac{\sqrt{3}}{2}+\frac{1}{2}]$

Q. Find the magnetic field at point $P$ due to a straight wire segment $AB$ of length $6\text{cm}$ carrying a current of $5\text{A}$.

1. $2.0\times {10}^{-5}\text{T}$
2. $1.5\times {10}^{-5}\text{T}$
3. $3.0\times {10}^{-5}\text{T}$
4. $2.5\times {10}^{-5}\text{T}$

Q. Two infinitely long parallel wires carry equal current in same direction. The magnitude of magnetic field at a mid point in between the two wires is

$[$1 Mark$]$

1. $\sqrt{2}$ times magnitude of the magnetic field produced due to each wire.
2. half of the magnitude of the magnetic field produced due to each wire.
3. twice the magnitude of the magnetic field produced due to each wire.
4. zero

Q. An infinitely long wire carrying current $I$ , is bent at right angle as shown in figure. Find the magnetic field at point $\text{P}$ located $x$ distance from $\text{O}$ as shown in the figure.

1. $\frac{{\mu }_{0}I}{2\pi x}$
2. $\frac{{\mu }_{0}I}{4\pi x}$
3. $\frac{{\mu }_{0}I}{2\sqrt{2}\pi x}$
4. None of these

Q. A solid cylinder wire of radius $R$ carries a current $I$. The magnetic field is $5\mu \text{T}$ at a point, which is $2R$ distance away from the axis of wire. Magnetic field at a point which is $\frac{R}{3}$ distance inside from the surface of the wire is

1. 
   $\frac{10}{3}\mu \text{T}$
2. 
   $\frac{20}{3}\mu \text{T}$
3. 
   $\frac{5}{3}\mu \text{T}$
4. 
   $\frac{40}{3}\mu \text{T}$

Q. Magnetic field due to two current elements having same currents in same direction at a point $\text{P}$ in between them is zero. If $r$ is the distance of point $\text{P}$ from one of the conductors and $d$ is the distance between both the conductors, then the value of $d$ is

1. $2r$
2. $4r$
3. $6r$
4. $r$

Q. A particle carrying charge equal to $100$ times the charge of an electron is performing one rotation per second in a circular path of radius $0.8\text{m}$. The value of magnetic field produced at the centre will be
( ${\mu }_0=$ permeability for vaccum )

1. $\frac{{10}^{-7}}{{\mu }_0}\text{T}$
2. ${10}^{-17}{\mu }_0\text{T}$
3. ${10}^{-6}{\mu }_0\text{T}$
4. ${10}^{-16}{\mu }_0\text{T}$

Q. The magnitude of the magnetic field at the centre of an equilateral triangular loop of side $1\text{m}$ which is carrying a current of $10\text{A}$ is
[$\text{Take}{\mu }_0=4\pi \times {10}^{-7}{\text{NA}}^{-2}$]

1. $18\mu \text{T}$
2. $9\mu \text{T}$
3. $3\mu \text{T}$
4. $1\mu \text{T}$

Q.

Two long parallel straight wires, each carrying a current I are separated by a distance r. If the currents are in opposite directions, then the strength of the magnetic field at any point midway between the two wires is

1. 
   

2. 
   

3. 
   

4. Zero

Q. Figure shows an arrangement in which four long parallel wires carrying equal current are placed at the corners of a square. The direction of current is as shown, either into the plane or outwards. The magnetic field at the centre of the square is

1. $\frac{{\mu }_{0}I}{2\pi r}\sqrt{2}$
2. $\frac{{\mu }_{0}I}{\pi r}\sqrt{2}$
3. $\frac{4{\mu }_{0}I}{2\pi r}$
4. Zero

Q. A long straight wire carrying current of $30\text{A}$ is placed in an external uniform magnetic field of $4\times {10}^{-4}\text{T}$ parallel to the current. Find the magnitude of net magnetic field at point $2\text{cm}$ away from the wire.

1. $7\times {10}^{-4}\text{T}$
2. $1\times {10}^{-4}\text{T}$
3. $5\times {10}^{-4}\text{T}$
4. $6\times {10}^{-4}\text{T}$

Q. An infinitely long wire carries a current $I$ flowing towards positive $z$ - axis. Consider a circle in $x-y$ plane with centre at $(2\text{m},0,0)$ and radius $1\text{m}$ as shown in figure.

The maximum value of path integral $\oint \overrightarrow{B}.\overrightarrow{dl}$ of the magnetic field $\overrightarrow{B}$ due to current carrying wire between two points $\text{P}$ & $\text{Q}$ lying along the circular path is

1. $\frac{{\mu }_{0}I}{12}$
2. $\frac{{\mu }_{0}I}{8}$
3. $\frac{{\mu }_{0}I}{6}$
4. Zero

Q. Consider the current carrying loop shown in the figure formed by the combination of radial wires and segment of circle whose center is at point $\text{O}$. Find the magnitude of $\overrightarrow{B}$ at point $\text{O}$.

1. $\frac{1}{4}[\frac{{\mu }_{0}I}{2a}-\frac{{\mu }_{0}I}{2b}]$
2. $\frac{1}{2}[\frac{{\mu }_{0}I}{2a}-\frac{{\mu }_{0}I}{2b}]$
3. $\frac{1}{6}[\frac{{\mu }_{0}I}{2a}-\frac{{\mu }_{0}I}{2b}]$
4. None of these

Q. Two very long, straight, and insulated wires are kept at $90°$ angle from each other in $xy-$plane as shown in figure.


These wires carry currents of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $\text{P}$ will be:

1. $\frac{+{\mu }_{0}I}{\pi d}\left(\hat{z}\right)$
2. $-\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$
3. Zero
4. $\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$

Q. The figure shows two long parallel current carrying wires separated by a distance $5\text{m}$. The magnetic field at a point $\text{P}$, situated midway between the two wires will be

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

Q. Infinite number of straight wires each carrying current $I$ are equally placed as shown in figure. Adjacent wires have currents in opposite direction. Net magnetic field at point $P$ is :

1. $\frac{{\mu }_{0}I\ln 2}{4\pi \sqrt{3}a}\hat{k}$
2. $\frac{{\mu }_{0}I\ln 4}{4\pi \sqrt{3}a}\hat{k}$
3. $\frac{{\mu }_{0}I\ln 2}{4\pi \sqrt{3}a}(-\hat{k})$
4. zero

Q. As shown in the figure, two infinitely long, identical wires are bent by ${90}^{\circ }$ and placed in such a way that the segments $LP$ and $QM$ are along the $x-$ axis, while segments $PS$ and $QN$ are parallel to the $y-$ axis. If $OP=OQ=4\text{cm}$ and the magnitude of the magneticf field at $O$ is ${10}^{-4}\text{T}$ and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at $O$ will be
$({\mu }_0=4\pi \times {10}^{-7}{\text{NA}}^{-2}):$

1. $40\text{A}$ perpendicular into the page
2. $20\text{A}$ perpendicular into the page
3. $20\text{A}$ perpendicular out of the page
4. $40\text{A}$ perpendicular out of the page

Q. The magnetic field $B$ at a distance $r$ from a long straight wire carrying current varies with distance $r$ as shown in the figure.

1. 
2. 
3. 
4. 

Q. A long thin metallic strip of width ${}^{\prime }{b}^{\prime }$ carries a current $I$ along its length as shown in figure. Find the magnitude of magnetic field in the plane of the strip at a distance ${}^{\prime }{a}^{\prime }$ from its edge as shown in figure.

1. $\frac{{\mu }_0}{4\pi }\frac{2I}{b}{\log }_e[1-\frac{b}{a}]$
2. $\frac{{\mu }_0}{4\pi }\frac{2I}{b}{\log }_e[1+\frac{b}{a}]$
3. $\frac{{\mu }_0}{2\pi }\frac{2I}{b}{\log }_e[1-\frac{b}{a}]$
4. None of these

Q. Two infinite plane sheets $\text{A}$ and $\text{B}$ carrying current in same direction, and current per unit length are $5\text{A/m}$ and $\lambda \text{A/m}$ respectively. Find the value of $\lambda$ so that magnetic field at point $\text{P}$ is zero.

1. $2.5\text{A/m}$
2. $10\text{A/m}$
3. $5\text{A/m}$
4. $3.33\text{A/m}$

Q. A circular loop of radius $R$ carries current $I_2$ in a clockwise direction, as shown in the figure. The centre of the loop is at a distance $D$ above a long straight wire. What should be the magnitude and direction of the current $I_1$ in the straight wire so that the net magnetic field at the centre of the loop is zero?

1. $\frac{\pi D}{R}{I}_2(\to )$
2. $\frac{\pi D}{R}{I}_2(\leftarrow )$
3. $\frac{\pi D}{4R}{I}_2(\to )$
4. $\frac{\pi D}{4R}{I}_2(\leftarrow )$

Q. Find the magnitude of net magnetic field at point $\text{P}$ as shown in figure. If two loops of wire carry the same current of $10\text{mA}$, but the flow of current is in opposite directions. One loop has a radius of $R_1=50\text{cm}$ and the other loop has a radius of $R_2=100\text{cm}$. The distance of point $\text{P}$ from first loop is $0.25\text{m}$ and from second loop is $0.75\text{m}$.

[Take, $({0.25}^2+{0.5}^2{)}^{3/2}=0.175;(1+{0.75}^2{)}^{3/2}=1.95$]

1. $2.8\times {10}^{-7}\text{T}$
2. $5.77\times {10}^{-10}\text{T}$
3. $6.91\times {10}^{-7}\text{T}$
4. $8.75\times {10}^{-12}\text{T}$

Q. What is the direction of magnetic field at point $\text{O}$ due to current carrying wire $\text{PQ}$?

1. out of the plane i.e. $+Z$ axis
2. into the plane i.e. $-Z$ axis
3. can't be determined with the given data
4. in the plane i.e. $X-Y$ plane

Q. Magnetic field $40\text{cm}$ away from long straight wire carrying current $2\text{A}$ is $1.00\mu \text{T}$. At what distance, the magnetic field becomes $0.100\mu \text{T}$ ?

1. $100\text{cm}$ away from wire
2. $40\text{m}$ away from wire
3. $4\text{cm}$ away from wire
4. $4\text{m}$ away from wire

Q. A toroid has inner radius of $5\text{cm}$ and outer radius of $8\text{cm}$. A point $\text{P}$ is located inside the toroid at a distance of $5.5\text{cm}$ from the center of the toroid. The toroid carries a current $I$ and magnetic field at point $\text{P}$ is equal to $B$ due to this current. If the toroid suddenly shrinks such that its inner radius becomes $3.5\text{cm}$ and outer radius becomes $7\text{cm}$, keeping the current and number of turns same. What will be the value of magnetic field at point $\text{P}$ in the later case ?

1. $B/2$
2. $B$
3. $B/3$
4. $2B$