JEE Advanced 1984
LEVELJEE Main
Visualized Solution
The Sigma Insight: Motion of a Charge in Magnetic Fields
Analyzing the Setup
Imagine you are observing a microscopic race track. Four different particles—a neutron, a proton, an electron, and an alpha particle—are shot upwards into a region where a uniform magnetic field is pointing directly into your screen.
Because they all enter with the exact same velocity, the only things dictating their paths are their intrinsic properties: mass and charge.
Our mission is to play detective and match each particle to its corresponding track (A, B, C, or D) left behind in the magnetic field.
The Master Equation
To solve this mystery, we need our trusty tool: the Lorentz force law. When a charged particle moves through a magnetic field, it experiences a magnetic force given by:
This elegant equation tells us two crucial things. First, the magnitude of the force depends on the charge . Second, the direction of the force is determined by the cross product of velocity and magnetic field , scaled by the sign of the charge.
Identifying the Neutral and Negative Particles
Let's start with the easiest suspect: the neutron. As its name suggests, a neutron is electrically neutral, meaning .
Plugging this into our force equation, we get a magnetic force of exactly zero. Without any force to push or pull it, the neutron will simply coast straight through the magnetic field. Looking at our diagram, Track C is the only undeviated path. Therefore, Track C belongs to the neutron.
Next, let's apply the right-hand rule to find the direction of the force. Point your fingers upwards (direction of velocity ) and curl them into the screen (direction of magnetic field ). Your thumb points to the left. This is the direction of the force for a positive charge.
But what about the electron? It carries a negative charge (). The negative sign flips the direction of the force, meaning the electron will be pushed to the right.
Observing the tracks, Track D is the only one bending to the right. We have successfully identified the electron!
The Radius Showdown
Proton vs. Alpha Particle
Now we are left with the proton and the alpha particle. Both are positively charged, so they both experience a force to the left. This perfectly matches Tracks A and B. But which is which?
When a particle experiences a magnetic force perpendicular to its velocity, it moves in a circular path. The radius of this path is determined by the balance between the magnetic force and the required centripetal force:
Since all our particles have the same velocity and are in the same magnetic field , the radius is directly proportional to their mass-to-charge ratio:
Let's compare these ratios. A proton has a mass and a charge . So its ratio is simply .
An alpha particle is a helium nucleus. It consists of two protons and two neutrons, giving it a mass of roughly . It has two protons, so its charge is . Its mass-to-charge ratio is:
The alpha particle has a mass-to-charge ratio that is twice as large as the proton's!
Because of this larger ratio, the alpha particle will have a larger radius of curvature. It takes a wider, more sweeping turn. Looking at the remaining tracks, Track B clearly has a larger radius than Track A.
Therefore, the alpha particle follows Track B, and the proton follows Track A. The mystery is completely solved!
Similar Questions
JEE Advanced 2011
LEVELJEE Main
An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?
* Multiple Correct Options
(A)
They will never come out of the magnetic field region
(B)
They will come out travelling along parallel paths
(C)
They will come out at the same time
(D)
They will come out at different times
JEE Main 2018
LEVELJEE Main
An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii respectively, in a uniform magnetic field . The relation between is
(A)
(B)
(C)
(D)
LEVELJEE Main
Two particles and of masses and respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are and , respectively and the trajectories are as shown in the figure. Then
(A)
(B)
(C)
and
(D)
and
JEE Main 2021
LEVELJEE Main
A proton, a deuteron and an -particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is ......... and their speed is ......... in the ratio.
(A)
1 : 2 : 4 and 2 : 1 : 1
(B)
2 : 1 : 1 and 4 : 2 : 1
(C)
4 : 2 : 1 and 2 : 1 : 1
(D)
1 : 2 : 4 and 1 : 1 : 2
JEE Advanced 1997
LEVELJEE Main
A proton, a deutron and an -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If and denote, respectively the radii of the trajectories of these particles, then
(A)
(B)
(C)
(D)
LEVELJEE Main
If an electron and a proton having same momenta enter perpendicularly to a magnetic field, then
(A)
curved path of electron and proton will be same (ignoring the sense of revolution)
(B)
they will move undeflected
(C)
curved path of electron is more curved than that of proton
(D)
path of proton is more curved
JEE Advanced 2017
LEVELJEE Advanced
Comprehension Passage
A charged particle (electron or proton) is introduced at the origin () with a given initial velocity . A uniform electric field and a uniform magnetic field exist everywhere. The velocity , electric field and magnetic field are given in columns 1, 2 and 3, respectively. The quantities are positive in magnitude.
$\begin{array}{lll}
\hline \text{Column 1} & \text{Column 2} & \text{Column 3} \\
\hline \text{(I) Electron with } \mathbf{v} = 2\frac{E_0}{B_0}\hat{x} & \text{(i) } \mathbf{E} = E_0\hat{z} & \text{(P) } \mathbf{B} = -B_0\hat{x} \\
\text{(II) Electron with } \mathbf{v} = \frac{E_0}{B_0}\hat{y} & \text{(ii) } \mathbf{E} = -E_0\hat{y} & \text{(Q) } \mathbf{B} = B_0\hat{x} \\
\text{(III) Proton with } \mathbf{v} = 0 & \text{(iii) } \mathbf{E} = -E_0\hat{x} & \text{(R) } \mathbf{B} = B_0\hat{y} \\
\text{(IV) Proton with } \mathbf{v} = 2\frac{E_0}{B_0}\hat{x} & \text{(iv) } \mathbf{E} = E_0\hat{x} & \text{(S) } \mathbf{B} = B_0\hat{z} \\
\hline
\end{array}$
Question 1:
In which case would the particle move in a straight line along the negative direction of Y-axis (i.e. move along )?
(A)
(IV) (ii) (S)
(B)
(II) (iii) (Q)
(C)
(III) (ii) (R)
(D)
(III) (ii) (P)
Question 2:
In which case will the particle move in a straight line with constant velocity?
(A)
(II) (iii) (S)
(B)
(III) (iii) (P)
(C)
(IV) (i) (S)
(D)
(III) (ii) (R)
Question 3:
In which case will the particle describe a helical path with axis along the positive z-direction?
(A)
(II) (ii) (R)
(B)
(III) (iii) (P)
(C)
(IV) (i) (S)
(D)
(IV) (ii) (R)
JEE Advanced 2004
LEVELJEE Main
A proton and an alpha particle, after being accelerated through same potential difference, enter uniform magnetic field, the direction of which is perpendicular to their velocities. Find the ratio of radii of the circular paths of the two particles.
JEE Advanced 2017
LEVELJEE Advanced
A uniform magnetic field exists in the region between and (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge and momentum directed along -axis enters region 2 from region 1 at point . Which of the following option(s) is/are correct?
* Multiple Correct Options
(A)
When the particle re-enters region 1 through the longest possible path in region 2, the magnitude of the change in its linear momentum between point and the farthest point from -axis is .
(B)
For , the particle will enter region 3 through the point on -axis.
(C)
For , the particle will re-enter region 1.
(D)
For a fixed , particles of same charge and same velocity , the distance between the point and the point of re-entry into region 1 is inversely proportional to the mass of the particle.
LEVELJEE Main
In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a
(A)
helix
(B)
straight line
(C)
ellipse
(D)
circle