Force on a Finite Wire

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

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

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.

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. 8 A

2. 6 A

3. 4 A

4. 2 A

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 with the direction of the field. It experiences a force of magnitude

[MP PET 1993]

1. 

2. 

3. 

4. 

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. 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 circular coil having mass $m$ is kept above the ground (x–z plane) at some height. The coil carries a current $i$ in the direction shown in figure. In which direction a uniform magnetic field $B$ should be applied so that the magnetic force balances the weight of the coil?

1. x. direction
2. y-direction
3. z-direction
4. None of these

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. Find the force and torque on the wire AB due to the infinitely long wire. Neglect gravity.

1. $\frac{{\mu }_0{i}^2}{2\pi },lo{g}_e\left(\frac{a+l}{a}\right),\frac{{\mu }_0{i}^{2}l}{2\pi }$
2. $zero,\frac{{\mu }_0{i}^{2}l}{2\pi }$
3. $\frac{{\mu }_0{i}^2}{2\pi }ln\left(\frac{l}{a}\right),\frac{{\mu }_0{i}^{2}l}{2\pi }$
4. $\frac{{\mu }_0{i}^2}{2\pi }ln\left(\frac{l+a}{q}\right),zero$

Q. A wire abc is carrying current I. It is bent as shown in the figure and is placed in a uniform magnetic field B. Length ab = l and $\angle abc={45}^{\circ }$. What is the ratio of force on bc to that on ab?

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

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. 8 A

2. 6 A

3. 4 A

4. 2 A