Force on a Finite Wire

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. $\frac{iBL}{\pi }$
2. $iBL\pi$
3. $2iBL$

4. $Zero$

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. 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. South
3. East
4. West

Q. A closed loop $PQRS$ carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments $PS,SR$ and$RQ$ 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

Q. A conductor PQRSTU, each side of length L, bent as shown in the figure, carries a current i and is placed in a uniform magnetic induction B directed parallel to the positive Y-axis. The force experience by the wire and its direction are

1. 2iBL directed along the negative Z-axis
2. 5iBL directed along the positive Z-axis
3. iBL direction along the positive Z-axis
4. 2iBL directed along the positive Z-axis

Q. A uniform conducting rectangular loop of sides $l$, $b$ and mass $m$ carrying current $i$ is hanging horizontally with the help of two vertical strings. There exists a uniform horizontal magnetic field B which is parallel to the longer side of the loop. The value of tension which is least is

1. $\frac{mg-iBb}{2}$
2. $\frac{mg+iBb}{2}$
3. $\frac{mg-2iBb}{2}$
4. $\frac{mg+2iBb}{2}$

Q. A 0.5m wire, stretched horizontally, carries a current of 10A from east to west in a magnetic field 0.1T directed – vertically downwards. The magnitude and direction of the force on the wire are

1. 0.5N, towards South
2. 0.5 N, towards north
3. 0.25N, towards south
4. 0.25 towards north

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 wire in shape of thin cylindrical shell carries current i as shown in figure.

1. If current is switched off, crossection area of wire increases.
2. Force exerted by half wire on the other half per unit length is $\frac{{\mu }_0{I}^2}{4{\pi }^{2}R}$.
3. Force exerted by half wire on other half per unit length is $\frac{{\mu }_0{I}^2}{16{\pi }^{2}R}$.
4. Magnetic field inside the wire is zero.

Q.

Figure shows a rod PQ of length 20 cm and mass 200 g suspended through a fixed point O by two threads of length 20 cm each. A magnetic field of strength 0.5 T exists in the vicinity of the wire PQ as shown in the figure. The wires connecting PQ with the battery are loose and exert no force on PQ. A current of 2 A is established when the switch S is closed. The tension in the threads is

1. 1.25 N

2. 2. 25 N

3. 3. 25 N

4. 4. 25 N

Q. A wire $\text{abcdef}$ with each side of length $l$ is bent as shown in figure. It carries a current $I$. It is placed in a uniform magnetic field $B$ parallel to y direction. what is the magnetic force experienced by wire ?

1. $BIl$ , along $-y$ direction
2. $2BIl$, along $+y$ direction
3. $BIl$, along $-x$ direction
4. $2BIl$, along $-x$ direction