Force on a Finite Wire

Q.

Dimensional formula for inductance

Q. A current carrying closed loop, in the form of a right-angled isosceles triangle $\text{ABC}$, is placed in a uniform magnetic field directed alongside $\text{AB}$. If the magnetic force on the arm $\text{BC}$ is $F$, the force on the arm $\text{AC}$ is

1. $-F$
2. $F$
3. $F\sqrt{2}$
4. $-F\sqrt{2}$

Q. An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current $i$ along the same direction is shown in fig. Magnitude of force per unit length on the middle wire 'B' is given by

1. $\frac{{\mu }_0{i}^2}{\sqrt{2}\pi d}$
2. $\frac{{\mu }_0{i}^2}{2\pi d}$
3. $\frac{2{\mu }_0{i}^2}{\pi d}$
4. $\frac{\sqrt{2}{\mu }_0{i}^2}{\pi d}$

Q. The variation of electric field between two charges $q_1$ and $q_2$ along the line joining the charges is plotted against the distance $r$ from $q_1$ (taking the direction from $q_1$ to $q_2$ as positive) as shown in the figure. Find the correct statement among the following is

1. $q_1$ and $q_2$ are positive and $|q_1|<|q_2|$
2. $q_1$ and $q_2$ are positive and $|q_1|>|q_2|$
3. $q_1$ is positive and $q_2$ is negative $|q_1|<|q_2|$
4. $q_1$ and $q_2$ are negative and $|q_1|<|q_2|$

Q. A closed loop $PQRS$ carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments $PS,SR$ and $RS$ are $F_1,F_2$ and $F_3$ respectively and are in the plane of the paper and along the directions shown, the force on the segment $QP$ is

1. $F_3-F_1+F_2$
2. $F_3-F_1-F_2$
3. $\sqrt{{(F_3-F_1)}^2+F_2^2}$
4. $\sqrt{{(F_3-F_1)}^2-F_2^2}$

Q. A vertical wire carrying a current in the upward direction is placed in a horizontal magnetic field directed towards north. The wire will experience a force directed towards

1. North
2. West
3. South
4. East

Q. A wire carrying a current i is kept in X-Y plane along the curve Y=A $sin\left(\frac{2\pi }{\lambda }x\right)$. A magnetic field B exists in the Z-direction as shown. Find the magnitude of the magnetic force on the portion of the wire between x=0 and $x=\lambda$

1. Zero
2. $i\lambda B$
   
3. $\frac{i\lambda B}{2}$
   
4. $\frac{3}{2i\lambda B}$

Q. A square of side of $2.0\text{m}$ is placed in a uniform magnetic field $\overrightarrow{B}=2.0\text{T}$ in a direction perpendicular to the plane of the square inwards. Equal current $i=3.0\text{A}$ is flowing in the directions shown in figure. Find the magnitude of magnetic force acting on the loop $ABCD$.

1. $18\sqrt{2}\text{N}$
2. $27\sqrt{2}\text{N}$
3. $36\sqrt{2}\text{N}$
4. $16\sqrt{2}\text{N}$

Q. 3 A of current is flowing in a linear conductor having a length of 40 cm. The conductor is placed in a magnetic field of strength 500 gauss and makes an angle of ${30}^{\circ }$ with the direction of the field. It experiences a force of magnitude

1. $3\times {10}^{4}N$.
2. $3\times {10}^{2}N$.
3. $3\times {10}^{-2}N$.
4. $3\times {10}^{-4}N$.

Q. Consider the situation shown in figure. If the lines are drawn in proportion to the charge, what is the ratio $\frac{|q_1|}{|q_2|}$ ?

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

Q. A conducting rod of length $l$ and mass $m$ is moving down a smooth inclined plane of inclination $\theta$ with constant velocity $v$. A current $I$ is flowing in the conductor in a direction perpendicular to the paper inwards. A vertically upward magnetic field $\overrightarrow{B}$ exists in space. Then, magnitude of magnetic field $\overrightarrow{B}$ is

1. $\frac{mg}{Il}\sin \theta$
2. $\frac{mg}{Il}\tan \theta$
3. $\frac{mg\cos \theta }{Il}$
4. $\frac{mg}{Il\sin \theta }$

Q. Same current $I=2A$ is flowing in a wire frame as shown in the figure. The frame is combination of two equilateral triangles ACD and CDE of side $1m$. It is placed in a uniform magnetic field $B=4T$ acting perpendicular to the plane of frame. The magnitude of magnetic force acting on the frame is

1. $24N$
2. Zero
3. $16N$
4. $8N$

Q.

A wire carrying a current i is placed in a uniform magnetic field in the form of the curve $y=asin\left(\frac{\pi x}{L}\right)0\le x\le 2L.$ The force acting on the wire is

1. 
   

2. 
   

3. 
   

4. Zero

Q. A straight conducting rod of length $30\text{cm}$ and having a resistance of $0.2\Omega$ is allowed to slide over two parallel thick metallic rails with uniform velocity of $0.2{\text{ms}}^{-1}$ as shown in the figure. The rails are stacked in a horizontal plane. If the horizontal component of earth's magnetic field is $0.3\times {10}^{-4}\text{T}$ and a steady current of $3\mu \text{A}$ is induced through the rod. The angle of dip will be

1. ${\tan }^{-1}\left(\frac{1}{3}\right)$
2. ${\tan }^{-1}\left(\sqrt{3}\right)$
3. ${\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
4. ${\tan }^{-1}\left(\frac{3}{4}\right)$

Q. A uniform magnetic field $\overrightarrow{B}=B_o\hat{k}$ exists in a region . A current carrying wire is placed in $x-y$ plane as shown in the figure. The magnetic force acting on the part $\text{AB}$ of wire is:

1. $2B_{o}ia\hat{i}$
2. $-3B_{o}ia\hat{j}$
3. $-3B_{o}ia\hat{k}$
4. $-B_{o}ia\hat{j}$

Q. Find electric field due to finite line charge at point $P$.

1. $55\text{N/C}$
2. $65\text{N/C}$
3. $75\text{N/C}$
4. $85\text{N/C}$

Q. A current carrying wire LN is bent in the from shown below. If wire carries a current of 10A and it is placed in a magnetic field of 5T which acts perpendicular to the paper outwards then it will experience a force

1. 5 N
2. Zero
3. 20 N
4. 30 N

Q.

Draw a labelled diagram of Van de Graaff generator. State its working principle to show how introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.

Q. The electric field $E$ is measured at a point $P(0,0,d)$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions.
Column-II describes different electric charge distributions, along with their locations. Match the functions in column-I with the related charge distributions in column-II.

column -I	column-II
(A) $E$ is independent of $d$	(P) A point charge $Q$ at the origin
(B) $E\propto \frac{1}{d}$	(Q) A small dipole with point charges $Q$ at $(0,0,l)$ and $-Q$ at $(0,0,-l)$. Take $2l<<<d$.
(C) $E\propto \frac{1}{d^2}$	(R) An infinite line charge coincident with the x- axis, with uniform linear charge density $\lambda$
(D) $E\propto \frac{1}{d^3}$	(S) Two infinite wire carrying uniform linear charge density parallel to the x-axis. The one along $(y=0,z=l)$ has a charge density $\lambda$ and the another along $(y=0,z=-l)$ has a charge density $-\lambda$. Take $2l<<d$.
	(T) Infinite plane charge coincident with the xy-plane with uniform surface charge density.

Which of the following option has the correct combiantion considering coulumn-I and column-II.

1. $A\to T$
2. $B\to S$
3. $C\to Q,R$
4. $D\to T$

Q. A conducting rod $PQ$ of length $l=1.0\text{m}$ is moving with a uniform speed $v=2\text{m/s}$ in a uniform magnetic field $B=4.0T$ directed into the paper. A capacitor of capacity $C=10\mu F$ is connected as shown in the figure. Then charge on plate $A$(in $\mu C$) is

Q.

A rectangular loop ABCD, carrying a current 15 A, is placed near a long wire carrying a current 40 A. The resultant force acting on the loop is

1. $6.4\times {10}^{-2}N$ directed away from wire

2. $6.4\times {10}^{-2}N$ directed towards wire

3. $3.6\times {10}^{-2}N$ directed away from wire

4. $3.6\times {10}^{-2}N$ directed towards the wire

Q. A metal strip $6.50\text{cm}$ long, $0.85\text{cm}$ wide moves with constant velocity $\overrightarrow{v}$ through a uniform magnetic field $B=1.20\text{mT}$, directed perpendicular to the strip, as shown in the figure. A potential difference of $3.90\mu \text{V}$ is measured between points $x$ and $y$ across the strip. Calculate the speed $v$.

1. $2.5\text{m/s}$
2. $5.5\text{m/s}$
3. $1.4\text{m/s}$
4. $0.4\text{m/s}$

Q.

A wire of mass m and length l can slide freely on a pair of smooth, vertical rails (figure 38-E31). A magnetic field B exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance C. Find the acceleration of the wire neglecting any electric resistance.

Q. A rod has a total charge $Q$, uniformly distributed along its length $L$. If the rod rotates with angular velocity $\omega$ about its end, compute its magnetic moment.

1. $\frac{Q\omega L^2}{2}$
2. $\frac{Q\omega L^2}{6}$
3. $\frac{Q\omega L^2}{3}$
4. $\frac{Q\omega L^2}{4}$

Q. A wire bent as shown in figure carries a current $i$ and is placed in a uniform field of magnetic induction $\overrightarrow{B}$ that emerges out from the plane of the figure.The magnetic force acting on the wire is:

1. $2BIR$
2. $4BIR$
3. $BIR$
4. $\frac{5}{2}BIR$

Q. A metal rod of mass $10\text{gm}$ and length $25\text{cm}$ is suspended on two springs as shown in figure. The springs are extended by $4\text{cm}$. When a 20 ampere current passes through the rod it rises by $1\text{cm}$. Determine the magnetic field assuming acceleration due to gravity be $10{\text{m/s}}^2$.

1. $5\text{T}$
2. $10\text{T}$
3. $0.5\times {10}^{-2}\text{T}$
4. $5\times {10}^{-2}\text{T}$

Q.

A steamboat goes across a lake and comes back

$\left(a\right)$ On a quiet day when the water is still and

$\left(b\right)$ On a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back.

If the speed of the launch on both days was the same, in which case it will complete the journey in lesser time

1. Case $\left(a\right)$

2. Case $\left(b\right)$

3. Same in both

4. Nothing can be predicted

Q.

A magnetic needle is placed in a uniform magnetic field and is aligned with the field. The needle is now rotated by an angle of ${60}^{\circ }$ and the work is W. The torque on the magnetic needle at this position is:

1. $\sqrt{3}W$

2. $2\sqrt{3}W$

3. $\frac{\sqrt{3}}{2}W$

Q.

Two long parallel wires carrying currents 2.5 A and "I" A in the same direction (directed in the o plane) are held at P and Q respectively as shown. The points P and Q are located at a distance of 5 m and 2 m respectively from a collinear point R. An electron moving with a velocity of $4\times {10}^{5}m{s}^{-1}$ along the positive x-axis experiences a force of magnitude $3.2\times {10}^{-20}N$ at the point R. The value of I is

1. 4 A

2. 8 A

3. 6 A

4. 2 A

Q. In the figure shown, the magnitude of magnetic force on the wire $ABC$ in the given uniform magnetic field will be:
$(B=2\text{Tesla})$

1. $4(3+2\pi )\text{N}$
2. $20\text{N}$
3. $30\text{N}$
4. $40\text{N}$