A Mysterious Force

Q. A uniform electric field and a uniform magnetic field are produced, pointed in the same direction. An electron is projected with its velocity pointing in the same direction

1. The electron will turn to its right
2. The electron will turn to its left
3. The electron velocity will increase in magnitude
4. The electron velocity will decrease in magnitude

Q. A velocity selector consists of electric field $\overrightarrow{E}=E\hat{k}$ and magnetic field $\overrightarrow{B}=B\hat{j}$ with $B=12\text{mT}$. The value of $E$ required for an electron of energy $728\text{eV}$ moving along the positive $x$-axis to pass undeflected is (Given, mass of electron $=9.1\times {10}^{–31}\text{kg}$)

1. $9600{\text{kVm}}^{-1}$
2. $192{\text{mVm}}^{-1}$
3. $192{\text{kVm}}^{-1}$
4. $16{\text{kVm}}^{-1}$

Q. A electron having a charge $e$ moves with a velocity $v$ in positive $x-$direction. A magnetic field exists in the region in positive $y-$ direction. The force on the electron acts in:
(perpendicular outward direction is taken as positive $z-$ axis).

1. negative direction of $y-$ axis
2. positive direction of $y-$ axis
3. positive direction of $z-$ axis
4. negative direction of $z-$ axis

Q.

Positive charge Q is distributed uniformly over a circular ring of radius R . A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the center. Find the force on the particle. Assume x<<<<R

Q.

A charge q moves with a constant velocity v parallel to the lines of force of a uniform magnetic field B. The force experienced by the charge q is

1. zero

2. 

3. qvB

4. 

Q. A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (a and U0 are constants). Match the potential energies in column I to the corresponding statement(s) in column II.

Column I	Column II
(A) $U_1\left(x\right)=\frac{U_0}{2}{[1-{\left(\frac{x}{a}\right)}^2]}^2$	(P) The force acting on the particle is zero at x = a.
(B) $U_2\left(x\right)=\frac{U_0}{2}{\left(\frac{x}{a}\right)}^2$	(Q) The force acting on the particle is zero at x = 0.
(C) $U_3\left(x\right)=\frac{U_0}{2}{\left(\frac{x}{a}\right)}^2\exp [-{\left(\frac{x}{a}\right)}^2]$	(R) The force acting on the particle is zero at x = – a.
(D) $U_4\left(x\right)=\frac{U_0}{2}[\frac{x}{a}-\frac{1}{3}{\left(\frac{x}{a}\right)}^3]$	(S) The particle experiences an attractive force towards x = 0 in the region $|x|<a.$
	(T) The particle with total energy $\frac{U_0}{4}$can oscillate about the point x = – a.

1. $\left(A\right)\to (P,Q,T);\left(B\right)\to (Q,T)$
   $\left(C\right)\to (P,Q.R,S)$
   $\left(D\right)\to (P,R,T)$
2. $\left(A\right)\to (P,Q,R,T);\left(B\right)\to (Q,S)$
   $\left(C\right)\to (P,Q.R,S)$
   $\left(D\right)\to (P,R,T)$
3. $\left(A\right)\to (P,Q,R,T);\left(B\right)\to (Q,S)$
   $\left(C\right)\to (P,Q.R,S)$
   $\left(D\right)\to (P,R,T)$
4. $\left(A\right)\to (P,Q,R,T);\left(B\right)\to (Q,S)$
   $\left(C\right)\to (P,Q,S,T)$
   $\left(D\right)\to (P,R,S)$

Q. A charged particle of mass $m$ and charge $q$, moving under the influence of a uniform electric field $E\hat{i}$ and a uniform magnetic field $B\hat{k}$, follows a trajectory from point $P$ to $Q$ as shown in figure. The velocities at $P$ and $Q$ are respectively, $v\hat{i}\text{and}-2v\hat{j}$. Then, which of the following statements (A, B, C, D) are correct? (Trajectory shown is schematic and not to scale)


$\left(A\right)$ $E=\frac{3}{4}\left(\frac{m{v}^2}{qa}\right)$
$\left(B\right)$ Rate of work done by the electric field at $P$ is $\frac{3}{4}\left(\frac{m{v}^2}{a}\right)$.
$\left(C\right)$ Rate of work done by both the fields at $Q$ is zero.
$\left(D\right)$ The difference between the magnitude of angular momentum of the particle at $P$ and $Q$ is $2mav$.

1. $A,C,D$
2. $B,C,D$
3. $A,B,C$
4. $A,B,C,D$

Q. an electron moving on a circular orbit of radius r with speed v. it produces a magnetic field B at its centre, then radius of circle is proportional to

Q.

Which of the following does not affect the motion of a moving electron?

1. Electric field applied perpendicular to the direction of motion

2. Electric field applied in the direction of motion

3. Magnetic field applied in the direction of motion

4. Magnetic field applied perpendicular to the direction of motion

Q. a particle of mass m carrying charge q is accelerated by a potential difference V. it enters perpendicularly in a region of uniform magnetic field B and executes circular arc of radius R, then q/m equals

Q. A particle of charge +q and mass m moving under the influence of a uniform electric field $E\hat{i}$ and a uniform magnetic field $B\hat{k}$ follows trajectory from P to Q as shown in figure. The velocities at P and Q are $v\hat{i}$ and $-2v\hat{j}$ respectively. Which of the following statement(s) is/are correct

1. Rate of work done by electric field at P is zero
2. Rate of work done by both the fields at Q is non zero
3. $E=\frac{3}{2}\frac{m{v}^2}{qa}$
4. Rate of work done by electric field at P is $\frac{3}{4}\frac{m{v}^3}{a}$

Q. 49. A proton, deutron and an alpha particle accelerated through the same potential difference enters a region of uniform magnetic field, moving perpendicular to it. What is the ratio of their circular paths?

Q. A proton is projected with a speed of 2 * 10^6 m/sec at an angle of 60 degree to the x-axis. If a uniform magnetic field of 0.104 T is applied along y - axis. Calculate radius of helix and time period of proton

Q. In a region of space uniform electric field is present as $\overrightarrow{E}=E_0\hat{j}$ and uniform magnetic field is present as $\overrightarrow{B}=B_0\hat{k}$. An electron is released form rest at origin. Which of the following best represents the path followed by electron after release.

1. 
2. 
3. 
4. None of the above

Q. A negative charge is coming towards an observer. The direction of the magnetic field produced by it will be: (As seen by observer)

1. Clockwise
2. Anticlockwise
3. In the direction of motion of charge
4. In the direction opposite to motion of charge

Q.

You are given two identical looking bars A and B. One of them is a bar magnet, while the other is an iron bar. How will you distinguish them without using any other material?

Q. Two charges of $10\mu C\text{and}-20\mu C$ are separated by a distance of $20\text{cm}$. The distance of the point from $10\mu C$ where electric potential is zero, if it lies between them is

1. $\frac{3}{20}$ cm
   
2. $6.67$ cm
3. $10$ cm
4. $16$ cm

Q.

An object of mass m moves in a circular path of radius R under the action of a force of constant magnitude F. The kinetic energy of object is?

Q. An electron of mass $m=9.1\times {10}^{-31}\text{kg}$ charge $q=-1.6\times {10}^{-19}\text{C}$ experiences no deflection , if subjected to an electric field of $E=3.2\times {10}^5\text{V}/\text{m}$ and a magnetic field of $B=2.0\times {10}^{-3}\text{Wb}/{\text{m}}^2$. Both the fields are normal to the path of electron and to each other. If the electric field is removed, then the electron will revolve in an orbit of radius ?

1. $45\text{m}$
2. $4.5\text{m}$
3. $0.45\text{m}$
4. $0.045\text{m}$

Q.

What is the total number of magnetic lines of force crossing a surface called?

Q.

Does stress depend on Youngs modulus?

Q. A particle having charge $q$ and mass $m$ is released from rest at origin, in a region with uniform electric field of magnitude $E$ which is directed along the positive $x-$axis. The speed of the particle as it crosses point $x=x_0$ will be -

​​​​​​​$[$0.77 Mark$]$

1. $\sqrt{\frac{qE{x}_0}{m}}$
2. $\sqrt{\frac{2qE{x}_0}{m}}$
3. $\sqrt{\frac{qE}{m{x}_0}}$
4. $\sqrt{\frac{4qE{x}_0}{m}}$

Q. Which of the following statements is / are true?

1. The strength of a non contact force is independent of distance between the bodies
2. meteors that enter earth atmosphere burn up due to non -contact force
3. magnetic force is a non -contact force
4. Contact force are always observes then non-contact forces.

Q. A particle of mass $m$ and charge $q$ is fastened to one end of a string of length $l$. The other end of the string is fixed to the point $O$. The whole system lies on a frictionless horizontal plane. Initially, the mass is at rest at $A$. A uniform electric field in the direction shown is then switched on. The speed of the particle when it reaches $B$ is -

1. $\sqrt{\frac{2qEl}{m}}$
2. $\sqrt{\frac{qEl}{m}}$
3. $\sqrt{\frac{3qEl}{m}}$
4. $\sqrt{\frac{5qEl}{m}}$

Q.

A charge of +10 µC enters a uniform magnetic field parallel to its direction. What will happen to the charge?

1. Perform circular motion in a plane parallel to the field.

2. Perform circular motion in a plane perpendicular to the field.

3. Continue to move with acceleration

4. Move undeviated with constant velocity.

Q. ntA particle of mass M and charge Q moves with a constant velocity V along the positive X direction. It enters a region containing a uniform magnetic field B directed along the negative Z direction extending from X equal to a to X equal to b. Find out the minimum value of V required so that the particle can just enter the region X greater than b.n

Q. If a charge is placed at rest in an electric field, will its path be along a line of force? Discuss the situation when the lines of force are straight and when they are curved.

Q. A proton and an a-particle accelerated through the same potential difference enter in the region of uniform magnetic field with their velocities perpendicular to the field.Compare the radii of the circular path followed by them?

Q. The gravitational field in a region is given by $\overrightarrow{g}=[4\hat{i}+\hat{j}]Nk{g}^{-1}$. Work done by this field is zero when the particle moves along the line
(Choose the appropriate option)

1. $4y+x=2$
2. $x+y=5$
3. $y+4x=2$
4. All of the above

Q. What is the magnetic force experienced by a particle of charge 6 C entering perpendicularly in a uniform magnetic field of 5T with a speed of 3 m/