A charged particle is released from rest in a region of steady and uniform electric and magnetic fie

Q: Why doesn't the magnetic field make the particle go in a circle?

A magnetic field only makes a particle go in a circle if the particle is moving perpendicular to the field. Here, the particle moves parallel to the field, so the magnetic force is zero.

Q: Does the particle's speed stay constant?

No, the electric force continuously does work on the particle, causing it to accelerate and increase its speed along the straight line.

Q: What if the charge was negative instead of positive?

A negative charge would accelerate in the opposite direction of the electric field. However, its velocity would still be parallel (or anti-parallel) to the magnetic field, so the magnetic force would still be zero, resulting in a straight line.

Q: What if the particle was thrown with an initial velocity perpendicular to the fields?

In that case, the magnetic field would cause it to move in a circle, while the electric field would accelerate it forward, resulting in a helical path with increasing pitch.

Q: Is it possible for the magnetic force to ever be non-zero in this specific setup?

Only if some external force pushes the particle sideways so its velocity is no longer perfectly parallel to the magnetic field. As long as it's only influenced by these parallel fields from rest, the magnetic force stays zero.

Question

A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a

Options:

(A) straight line

(B) circle

(C) helix

(D) cycloid

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Imagine you are holding a tiny charged particle, perfectly still, in a region of space where both an electric field and a magnetic field exist. The special thing about this region is that both fields are pointing in the exact same direction. They are parallel.

When you release the particle from rest, it's like dropping a ball in gravity, but here, the "gravity" is the electric field. The particle has zero initial velocity.

### The Master Equation

To understand what happens next, we need to look at the forces that can act on our charged particle. There are two potential forces at play here: the electric force and the magnetic force.

The electric force is straightforward: $\mathbf{F}_e = q\mathbf{E}$. It only depends on the charge and the electric field.

The magnetic force is a bit more complex: $\mathbf{F}_m = q(\mathbf{v} 	imes \mathbf{B})$. It depends on the charge, the magnetic field, and crucially, the velocity of the particle.

### The Initial Push

At the exact moment you release the particle ($t = 0$), its velocity $\mathbf{v}$ is zero. Because the magnetic force requires velocity to act, it is completely zero at this instant.

However, the electric force doesn't care if the particle is moving or not. It immediately exerts a force $\mathbf{F}_e = q\mathbf{E}$ on the particle. This force causes the particle to accelerate in the direction of the electric field.

### The Magnetic Force Check

As the particle accelerates, it gains velocity. Because the only force acting on it is the electric force, the particle moves exactly along the electric field lines. So, its velocity vector $\mathbf{v}$ is parallel to the electric field $\mathbf{E}$.

But wait, the problem stated that the electric and magnetic fields are parallel! This means the velocity $\mathbf{v}$ is also parallel to the magnetic field $\mathbf{B}$.

Let's plug this back into our magnetic force equation. The cross product of two parallel vectors is always zero because the angle between them is $0^\circ$, and $\sin(0^\circ) = 0$. Therefore, $\mathbf{F}_m = qvB\sin(0^\circ) = 0$.

### Final Conclusion

Even though the particle is now moving through a magnetic field, the magnetic force remains zero for the entire journey. The electric force is the only force acting on the particle, continuously accelerating it in the same direction.

Since the force is always along the direction of motion, the particle will never turn or curve. It will simply move in a **straight line**.

Animated Solution for Physics - Magnetic Effects of Current: A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a

Select Answer:

Visualized Solution

$Visual Anchor$

$Force Equations$

$Initial Motion$

$Velocity Direction$

$Magnetic Force Check$

$Final Path$

$The Way Forward$

The Sigma Insight: Motion of a Charge in Magnetic Fields

Analyzing the Setup

The Master Equation

The Initial Push

The Magnetic Force Check

Final Conclusion

Similar Questions

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

Comprehension Passage

In which case would the particle move in a straight line along the negative direction of Y-axis (i.e. move along $- \overset{y}{^}$ )?

In which case will the particle move in a straight line with constant velocity?

In which case will the particle describe a helical path with axis along the positive z-direction?

For a positively charged particle moving in a $x - y$ plane initially along the $x$ -axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond $P$ . The curved path is shown in the $x - y$ plane and is found to be non-circular.

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then

A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $E$ and $B$ with a velocity $v$ perpendicular to both $E$ and $B$ and comes out without any change in magnitude or direction of $v$ . Then,

A charged particle moves through a magnetic field perpendicular to its direction. Then,

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?

If an electron and a proton having same momenta enter perpendicularly to a magnetic field, then