Analysis of Force Equation

Q.

A uniform magentic field exists in space. A particle of mass m and charges q is projected towards negative x-axis with speed v from a point (d, 0, 0). The maximum value of v for which the particle does not hit the y-z plane is

1. 2Bq/dm

2. Bqd/m

3. Bq/2dm

4. Bqd/2m

Q. $H{e}^{+}$ and $O^{2+}$ions (mass of $H{e}^{+}=4amu$ and that of $O^{2+}=16amu$) pass through a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then

1. Both the ions will be deflected equally
2. $H{e}^{+}$ions will be deflected more than $O^{2+}$ ions.
3. $H{e}^{+}$ions will be deflected less than $O^{2+}$ ions
4. No ions will be deflected

Q. A charge particle of specific charge q/m is projected perpendicular to magnetic as well as electric field ‘B' & 'E’.
['E' is parallel to 'B'.]

1. Path of the charged particle may be straight line.
2. Path of the charged particle is helix with increasing pitch.
3. Frequency of the charged particle increases.
4. Speed increases to thrice of its original speed in time $\frac{2\sqrt{2}{V}_{0}m}{qE}.$
   ($V_0$ is initial speed)

Q. Which particle will experience max magnetic force when projected with the same velocity perpendicular to a MF?

1. Electron
2. Proton
3. He+
4. Li++

Q.

What is the source of magnetism in materials?

Q. $H{e}^{+}$ and $O^{2+}$ions (mass of $H{e}^{+}=4amu$ and that of $O^{2+}=16amu$) pass through a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then

1. No ions will be deflected
2. Both the ions will be deflected equally
3. $H{e}^{+}$ions will be deflected less than $O^{2+}$ ions
4. $H{e}^{+}$ions will be deflected more than $O^{2+}$ ions.

Q. An ionised gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +ve x-axis and a magnetic field along the +z direction then

1. Positive ions deflect towards +y direction and negative ions towards – y direction
2. All ions deflect towards + y direction
3. All ions deflect towards – y direction
4. Positive ions deflect towards – y direction and negative ions towards + y direction.

Q. The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies with $\lambda$ as follows :

1. 
2. 
3. 
4. 

Q. An electron at rest is accelerated by a potential $V_1$ and it experiences a force ‘F’ in a uniform magnetc field.When it is accelerated by a potential $V_2$ the electron experiences a force 2F in the same field. The value of $\frac{V_1}{V_2}$ is

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

Q.

A square metal wire loop of side 10 cm and resistance 1 $\Omega$ is moved with a constant velocity v in a uniform magnetic field B = 2 T, as shown in Fig. 25.4. The loop is connected to 4 $\Omega$ resistor.
What should be the speed v of the loop as to have a steady current of 1 mA in the loop ?

1. $1cm{s}^{-1}$

2. $2cm{s}^{-1}$

3. $3cm{s}^{-1}$

4. $4cm{s}^{-1}$

Q. A circular ring of radius $R$ with uniform positive charge density $\lambda$ is fixed in the $y-z$ plane with its centre at the origin $O$. A particle of mass $m$ and charge $+q$ is projected from point $P$ $(\sqrt{3}R,0,0)$ on the positive $x$-axis directly towards $O$ with initial velocity $v$ such that the particle does not come back to $P$. The minimum value of $v$ is

1. $\sqrt{\frac{q\lambda }{2{ϵ}_{0}m}}$
   
2. $\sqrt{\frac{2q\lambda }{{ϵ}_{0}m}}$
3. $\sqrt{\frac{q\lambda }{{ϵ}_{0}m}}$
   
4. $\sqrt{\frac{3q\lambda }{2{ϵ}_{0}m}}$

Q. A charged particle of charge 4 mc enters a uniform magnetic field of induction $\overrightarrow{B}=4\overrightarrow{i}+y\overrightarrow{j}+z\overrightarrow{k}$ tesla with a velocity $\overrightarrow{V}=2\overrightarrow{i}+3\overrightarrow{j}-6\overrightarrow{k}$. If the particle continues to move undeviated, then the strength of the magnetic filed induction (B) is___ tesla.

1. 14
2. 2
3. 3.5
4. 28

Q. Which particle will experience max magnetic force when projected with the same velocity perpendicular to a MF?

1. Electron
2. Proton
3. He+
4. Li++

Q. A charged particle of charge 4 mc enters a uniform magnetic field of induction $\overrightarrow{B}=4\overrightarrow{i}+y\overrightarrow{j}+z\overrightarrow{k}$ tesla with a velocity $\overrightarrow{V}=2\overrightarrow{i}+3\overrightarrow{j}-6\overrightarrow{k}$. If the particle continues to move undeviated, then the strength of the magnetic filed induction (B) is___ tesla.

1. 14
2. 2
3. 3.5
4. 28

Q. A charge particle of specific charge q/m is projected perpendicular to magnetic as well as electric field ‘B' & 'E’.
['E' is parallel to 'B'.]

1. Path of the charged particle may be straight line.
2. Path of the charged particle is helix with increasing pitch.
3. Frequency of the charged particle increases.
4. Speed increases to thrice of its original speed in time $\frac{2\sqrt{2}{V}_{0}m}{qE}.$
   ($V_0$ is initial speed)

Q.

A uniform magentic field exists in space. A particle of mass m and charges q is projected towards negative x-axis with speed v from a point (d, 0, 0). The maximum value of v for which the particle does not hit the y-z plane is

1. 2Bq/dm

2. Bqd/m

3. Bq/2dm

4. Bqd/2m

Q. Two insulated conductors are charged by transferring electrons from one conductor to the other. A potential difference of $100\text{V}$ was produced by transferring $6.25\times {10}^{15}$ electrons from one conductor to the other. The capacitance of the system will be

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

Q. An electron at rest is accelerated by a potential $V_1$ and it experiences a force ‘F’ in a uniform magnetc field.When it is accelerated by a potential $V_2$ the electron experiences a force 2F in the same field. The value of $\frac{V_1}{V_2}$ is

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

Q. A beam consisting of protons and electrons passed through perpendicular MF.The protons and electrons,

1. Will go undeviated
2. Will be deviated by the same angle and will not separate.
3. Will be deviated by different angles and hence separate.
4. Will be deviated by the same angle and separate.

Q. A 2 MeV proton is moving perpendicular to a uniform magnetic field of 2.5 T. The force on the proton is (mass of proton = $1.6\times {10}^{-27}kg$)

1. $10\times {10}^{-12}N$
2. $8\times {10}^{-12}N$
3. $2.5\times {10}^{-10}N$
4. $8\times {10}^{-11}N$

Q. A particle with ${10}^{-11}$ coulomb of charge and ${10}^{-7}$ kg mass is moving with a velocity of ${10}^8$ m/s along the y-axis. A uniform static magnetic field B = 0.5 T is acting along the x-direction. The force on the particle is

1. $5\times {10}^{-11}Nalong\hat{i}$
2. $5\times {10}^{3}Nalong\hat{k}$
3. $5\times {10}^{-11}Nalong\hat{j}$
4. $5\times {10}^{-4}Nalong-\hat{k}$

Q. Figure below shows a conducting rod of negligible resistance that can slide on a smooth U-shaped rail made of a wire of resistance $1\Omega m^{-1}$. Position of the conducting rod at $t=0$ is shown. A time dependent magnetic field $B=2T\text{(tesla)}$ is switched ON at $t=0$.
Following the situation of the previous question, the magnitude of force required to move the conducting rod at a constant speed of $5{\text{cms}}^{-1}$ at the same instant $t=2s$ is equal to

1. 0.16 N
2. 0.12 N
3. 0.08 N
4. 0.06 N

Q. An electron is fired parallel to uniform Electric and Magnetic field acting in the same direction.Electron

1. Gains Energy
2. Loses Energy
3. Moves along a circular path
4. Moves along parabolic path

Q. A particle of mass m and charge q is released from rest in a vertical plane from height H. A uniform magnetic field also exist in horizontal direction. Magnitude of magnetic field is B. Then

1. Charge particle will never reach ground if $H>\frac{2m^{2}g}{(qB{)}^2}$
2. Vertical motion of charge particle will be SHM.
3. Maximum speed attained by particle is $\frac{2m}{qB}\sqrt{g}$
4. Motion of particle is oscillatory

Q. A charged particle passes undeviated through velocity vector if, v =particle velocity, E= Electric Field, B= Magnetic Field

1. v<E/B
2. v>E/B
3. v=E/B
4. None of these

Q. Two conducting rings $P$ and $Q$ of radius $r$ and $3r$ move in opposite directions with velocities $2v$ and $v$ respectively on a conducting surface $S$. There is a uniform magnetic field of magnitude $B$ perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

1. $\text{zero}$
2. $2Brv$
3. $6Brv$
4. $10Brv$