Q: Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

Current in wire A, \$I_1=8\ A\$Current in wire B, \$I_2=5\ A\$Force exerted on 10cm section of wire A,\$B=\dfrac{\mu_o2I_1I_2l}{4\pi r}=2\times 10^{-5}T\$Attractive force normal to A towards B, because current direction same.

Q: Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a \$25\ cm\$ length of wire \$C\$ is

Force on wire \$C\$ due to wire \$D\$\$F_D=10^{-7} \times \dfrac{2 \times 30 \times 10}{2 \times 10^{-2}} \times 25 \times 10^{-2}=5 \times 10^{-4}\ N\$ (towards right)Force on wire \$C\$ due to wire \$G\$\$F_G=10^{-7} \times \dfrac{2 \times 20 \times 10}{2 \times 10^{-2}} \times 25 \times 10^{-2}=5 \times 10^{-4}\ N\$ (towards left)\$\Rightarrow\$ Net force on wire \$C\$ is \$F_{net}=F_D- F_G=0\$

Q: Two long straight parallel conductors carry steady current \${ I }_{ 1 }\$ and \${ I }_{ 2 }\$ separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field set up in one produces an attractive force on the other. Obtain the expression for this force. Hence define one ampere.

Magnetic field due to wire a on b =\$\dfrac{\mu_0 I_a}{2\pi d}\$Force on a current carrying wire placed in magnetic field=\$I(\vec{l}\times \vec{B})\$Hence force on b is \$F_{ba}=I_bl\dfrac{\mu_0I_a}{2\pi d}\$The direction of force experienced by the wire 'a' is toward the wire 'b' as shown.Similarly the direction of force experienced by the wire 'b' is toward the wire Thus, the force is attractive.If two long wires are placed in vacuum at a separation of 1 m, one Ampere would be defined as the current in each wire that would produce a force of per unit length of wire.

Q: Two long straight wires are set parallel to each other at separation \$r\$ and each carries a current \$i\$ in the same direction. The strength of the magnetic field at any point midway between the two wires is

\$x=\dfrac{r}{2}\$\$B_1=-\dfrac{\mu_oi}{2\pi x}\$\$B_2=\dfrac{\mu_oi}{2\pi (r-x)}\$After putting the value of \$x=\dfrac{r}{2}\$ we get,\$B=B_1+B_2=0\$

Q: Through two parallel wires A and B, 10A and 2A of currents are passed respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2m, then force on the conductor B, which is situated at 10 cm distance from A, will be

\$\displaystyle F = \dfrac{\mu_0}{4 \pi} \dfrac{2 I_1 I_2}{r} \times l \$\$= \dfrac{10^{-7} \times 2 \times 10 \times 2}{0.1} \times 2 \$\$= 8 \times 10^{-5} N\$

Q: Two parallel very long straight wires carrying current of \$5\$A each are kept at a separation of \$1\$m. If the currents are in the same direction, the force per unit length between them is __________ N/m. \$(\mu_o=4\pi\times 10^{-7}SI)\$.

Given : \$I_1 = I_2 = 5 \ A\$ \$d = 1 \ m\$Force per unit length between them \$F = \dfrac{\mu_o I_1 I_2}{2\pi d}\$\$\therefore\$ \$F = \dfrac{4\pi\times 10^{-7}\times 5\times 5}{2\pi \times 1} = 5\times 10^{-6} \ N/m\$Since current flows in the same direction in the wires, so the wires attract each other.Correct answer is option B

Q: Two long parallel wires are at a distance of 1m. If both of them carry one ampere of current in same direction, then the force of attraction on unit length of the wires will be

Given: \$I_1= I_2 = 1\$ A Distance between the wires, \$d = 1\$ mForce of attraction per unit length, \$f = \dfrac{\mu_0 I_1 I_2}{2\pi d}\$ \$N/m\$\$\therefore \$ \$f = \dfrac{4\pi \times 10^{-7} \times (1) (1)}{2 \pi \times 1} = 2 \times 10^{-7}\$ \$N/m\$

Question 1

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

Accepted Answer

Current in wire A, $I_1=8\ A$Current in wire B, $I_2=5\ A$Force exerted on 10cm section of wire A,$B=\dfrac{\mu_o2I_1I_2l}{4\pi r}=2\times 10^{-5}T$Attractive force normal to A towards B, because current direction same.

Question 2

Two circular coils 1 and 2 are made from the same wire but the radius of 1st coil is twice that of the 2nd coil. What potential difference in volts should be applied across them so that the magnetic magnetic field at the centres is the same

Accepted Answer

Magnetic feild due to first coil and second coil is same at center.Then magnetic field $B$ at center is,$\ B=\dfrac { { \mu  }_{ 0 }{ I }_{ 1 } }{ 2(2r) } =\dfrac { \mu _{ 0 }{ I }_{ 2 } }{ 2(r) } =\dfrac { { I }_{ 1 } }{ { I }_{ 2 } } =2$ ..(1)As we know that Resistance of coil is related as,$R=\rho \dfrac {l}{A}$ where $\rho$=resistivity ,$l$=length ,$A$=area of cross section.$\rho$ and $A$ is same for both coil but $l_1=2 \pi(2r)$ and $l_2=2 \pi (r)$If $V_1$ and $V_2$ applied across first and second coil then,$I_1=\dfrac{V_1}{R_1}$ and $I_2=\dfrac{V_2}{R_2}$$I_1=\dfrac{V_1}{\rho \dfrac{l_1}{A}}$..(2)  and $I_2=\dfrac{V_2}{\rho \dfrac{l_2}{A}}$ ...(3)From (1),(2),(3),$\dfrac{V_1}{l_1} \times \dfrac{l_2}{V_2}=2$$\dfrac{V_1}{V_1} \times \dfrac{l_2}{l_1}=2$$\dfrac{V_1}{V_2} \times \dfrac{1}{2}=2$$\dfrac{V_1}{V_2}=4$$V_1=4V_2$

Question 3

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a $25\ cm$ length of wire $C$ is

Accepted Answer

Force on wire $C$ due to wire $D$$F_D=10^{-7} \times \dfrac{2 \times 30 \times 10}{2 \times 10^{-2}} \times 25 \times 10^{-2}=5 \times 10^{-4}\ N$ (towards right)Force on wire $C$ due to wire $G$$F_G=10^{-7} \times \dfrac{2 \times 20 \times 10}{2 \times 10^{-2}} \times 25 \times 10^{-2}=5 \times 10^{-4}\ N$ (towards left)$\Rightarrow$ Net force on wire $C$ is $F_{net}=F_D- F_G=0$

Question 4

Two long straight parallel conductors carry steady current $I_{1}$ and $I_{2}$ separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field set up in one produces an attractive force on the other. Obtain the expression for this force. Hence define one ampere.

Accepted Answer

Suppose two long thin straight conductors (or wires) $PQ$ and $RS$ are placed parallel to each other in vacuum (or air) carrying currents $I_1$ and $I_2$ respectively. It has been observed experimentally that when the currents in the wire are in the same direction., they experience an attractive force and when they carry currents in opposite directions, they experience a repulsive force.Let the conductors $PQ$ and $RS$ carry currents $I_1$ and $I_2$ in same direction and placed at separation $r$.Consider a current-element $'ab'$ of length $Delta L$ of wire $RS$. The magnetic field produce by current carrying conductor $PQ$ at the location of other wire $RS$$B_1=\dfrac {\mu_0 I_1}{2\pi r}.....(i)$According to maxwell's right hand rule or right hand palm rule number $1$, the direction of $B_1$ will be perpendicular to the plane of paper and direct downward. Due to this magnetic field, each element of other wire experiences a force. The direction of current element is perpendicular to the magnetic field; therefore the magnetic force on element $ab$ of length $\Delta L$$\Delta F=B_1 I_2\ \Delta L \sin 90^o =\dfrac {\mu_0 I_1}{2\pi r}I_2 \Delta L$$\therefore $ The total force on conductor of length $L$ will be$F=\dfrac {\mu_0 I_1I_2}{2\pi r}\displaystyle \sum \Delta L=\dfrac {\mu_0 I_1I_2}{2\pi r}L$$\therefore $ Force acting per unit length of conductor$f=\dfrac FL =\dfrac {\mu_0 I_1I_2}{2\pi r} N/m ....(ii)$According to Fleming's left hand rule, the direction of magnetic force will be towards $PQ$ i.r, the force will be attractive.On the other hand if the currents $I_1$ and $I_2$ wires are in opposite direction, the force will be repulsive. The magnitude of force in each case remains the same.Definition of $SI$ unit of Current (ampere): In $SI$ system of fundamental unit of current 'ampere ' is defined assuming the force between the two current carrying wires as standard.The force between two parallel current carrying conductors $r$ is$f=\dfrac {F}{L}=\dfrac {\mu_0 I_1 I_2}{2\pi r}N/m$If $I_1=i_2=1\ A, r=1\ m$, then$f=\dfrac {\mu_0}{2\pi }=2\times 10^{-2}N/m$Thus $1$ ampere is the current which when flowing in each of parallel conductors placed at separation $1\ m$ in vacuum exert a force of $2\times 10^{-7}$ on $1\ m$ length of either wire.

Question 5

Two long straight parallel conductors carry steady current $I_{1}$ and $I_{2}$ separated by a distance $d$ . If the currents are flowing in the same direction, show how the magnetic field set up in one produces an attractive force on the other.
Obtain the expression for this force. Hence define one ampere.

Accepted Answer

Magnetic field due to wire a on b =$\dfrac{\mu_0 I_a}{2\pi d}$Force on a current carrying wire placed in magnetic field=$I(\vec{l}\times \vec{B})$Hence force on b is $F_{ba}=I_bl\dfrac{\mu_0I_a}{2\pi d}$The direction of force experienced by the wire 'a' is toward the wire 'b' as shown.Similarly the direction of force experienced by the wire 'b' is toward the wire Thus, the force is attractive.If two long wires are placed in vacuum at a separation of 1 m, one Ampere would be defined as the current in each wire that would produce a force of per unit length of wire.

Question 6

Two long straight wires are set parallel to each other at separation $r$ and each carries a current $i$ in the same direction. The strength of the magnetic field at any point midway between the two wires is

Accepted Answer

$x=\dfrac{r}{2}$$B_1=-\dfrac{\mu_oi}{2\pi x}$$B_2=\dfrac{\mu_oi}{2\pi (r-x)}$After putting the value of $x=\dfrac{r}{2}$ we get,$B=B_1+B_2=0$

Question 7

Through two parallel wires A and B, 10A and 2A of currents are passed respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2m, then force on the conductor B, which is situated at 10 cm distance from A, will be

Accepted Answer

$\displaystyle F = \dfrac{\mu_0}{4 \pi} \dfrac{2 I_1 I_2}{r} \times l $$= \dfrac{10^{-7} \times 2 \times 10 \times 2}{0.1} \times 2 $$= 8 \times 10^{-5} N$

Question 8

Two parallel very long straight wires carrying current of $5$A each are kept at a separation of $1$m. If the currents are in the same direction, the force per unit length between them is __________ N/m. $(\mu_o=4\pi\times 10^{-7}SI)$.

Accepted Answer

Given :  $I_1 = I_2 = 5 \ A$                $d = 1 \ m$Force per unit length between them    $F = \dfrac{\mu_o I_1 I_2}{2\pi d}$$\therefore$  $F = \dfrac{4\pi\times 10^{-7}\times 5\times 5}{2\pi \times 1} = 5\times 10^{-6} \ N/m$Since current flows in the same direction in the wires, so the wires attract each other.Correct answer is option B

Question 9

Two long parallel wires are at a distance of 1m. If both of them carry one ampere of current in same direction, then the force of attraction on unit length of the wires will be

Accepted Answer

Given: $I_1= I_2 = 1$ A              Distance between the wires, $d = 1$ mForce of attraction per unit length, $f = \dfrac{\mu_0  I_1 I_2}{2\pi  d}$   $N/m$$\therefore $    $f = \dfrac{4\pi \times 10^{-7}   \times (1) (1)}{2 \pi  \times 1}  = 2 \times 10^{-7}$ $N/m$

Question 10

Three long straight wires A, B and C are carrying currents as shown in figure. Then the resultant force on B is directed :

Accepted Answer

Hint:If the current in the two parallel wires is in the same direction then the wires attract each other.Step 1: Expression of force between two parallel wires,The force between two parallel wires having current $I_1$ and $I_2$ and separated by distance $d$ is,$F=\frac{\mu_oI_1 I_2}{2\pi d}$Therefore,$F\propto I_1I_2$ and $F\propto \frac{1}{d}$Step 2: Find the stronger force.Wire A and wire C are trying to pull wire B towards them.The separation between the wires for both cases is the same.$I_A I_B=(1A)(2A)=3A^2$$I_c I_B=(3A)(2A)=6A^2$$\because$ $F\propto I_1I_2$$\therefore$ $F_{BC}>F_{AB}$Therefore wire is pulled towards $C$.$\textbf{Hence option D correct}$

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Force between Parallel Current carrying Wire

Definition of Ampere Using Two Current Carrying Parallel Conductors

Roget's Spiral to Show Attraction Between Parallel Currents

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

Two circular coils 1 and 2 are made from the same wire but the radius of 1st coil is twice that of the 2nd coil. What potential difference in volts should be applied across them so that the magnetic magnetic field at the centres is the same

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a $25 c m$ length of wire $C$ is

Two long straight wires are set parallel to each other at separation $r$ and each carries a current $i$ in the same direction. The strength of the magnetic field at any point midway between the two wires is

Through two parallel wires A and B, 10A and 2A of currents are passed respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2m, then force on the conductor B, which is situated at 10 cm distance from A, will be

Two parallel very long straight wires carrying current of $5$ A each are kept at a separation of $1$ m. If the currents are in the same direction, the force per unit length between them is __________ N/m. $(μ_{o} = 4 π \times 1 0^{- 7} S I)$ .

Two long parallel wires are at a distance of 1m. If both of them carry one ampere of current in same direction, then the force of attraction on unit length of the wires will be

Three long straight wires A, B and C are carrying currents as shown in figure. Then the resultant force on B is directed :

Revise with Concepts

Advanced Knowledge of Force Between Two Current Carrying Parallel Wires

Quick Summary With Stories

Force between Parallel Current carrying Wire

Definition of Ampere Using Two Current Carrying Parallel Conductors

Roget's Spiral to Show Attraction Between Parallel Currents

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

Two circular coils 1 and 2 are made from the same wire but the radius of 1st coil is twice that of the 2nd coil. What potential difference in volts should be applied across them so that the magnetic magnetic field at the centres is the same

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is

Two long straight wires are set parallel to each other at separation r and each carries a current i in the same direction. The strength of the magnetic field at any point midway between the two wires is

Through two parallel wires A and B, 10A and 2A of currents are passed respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2m, then force on the conductor B, which is situated at 10 cm distance from A, will be

Two parallel very long straight wires carrying current of 5A each are kept at a separation of 1m. If the currents are in the same direction, the force per unit length between them is __________ N/m. (μo​=4π×10−7SI).

Two long parallel wires are at a distance of 1m. If both of them carry one ampere of current in same direction, then the force of attraction on unit length of the wires will be

Three long straight wires A, B and C are carrying currents as shown in figure. Then the resultant force on B is directed :

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a $25 c m$ length of wire $C$ is

Two long straight wires are set parallel to each other at separation $r$ and each carries a current $i$ in the same direction. The strength of the magnetic field at any point midway between the two wires is

Two parallel very long straight wires carrying current of $5$ A each are kept at a separation of $1$ m. If the currents are in the same direction, the force per unit length between them is __________ N/m. $(μ_{o} = 4 π \times 1 0^{- 7} S I)$ .