In a region, steady and uniform electric and magnetic fields are present. These two fields are paral

Q: Why doesn't the magnetic field exert a force initially?

The magnetic force on a charged particle is given by $\mathbf{F}_m = q(\mathbf{v} \times \mathbf{B})$. Since the particle is released from rest, its initial velocity $\mathbf{v}$ is zero, making the magnetic force zero.

Q: Does the magnetic field ever exert a force in this scenario?

No. Even as the particle gains velocity due to the electric field, its velocity vector $\mathbf{v}$ is parallel to the magnetic field $\mathbf{B}$. The cross product of parallel vectors is zero ($\sin 0^\circ = 0$), so the magnetic force remains zero throughout the motion.

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

If the initial velocity had a component perpendicular to the magnetic field, the magnetic field would exert a force, causing the particle to move in a circular or helical path depending on the exact initial conditions.

Q: Does the mass of the particle affect its path here?

The mass affects the rate of acceleration ($a = qE/m$), but it does not change the shape of the path. The path will remain a straight line regardless of the mass.

Q: What if the charge was negative?

A negative charge would experience an electric force in the opposite direction to the electric field. It would accelerate in a straight line in the opposite direction, but the path would still be a straight line.

Question

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

Options:

(A) helix

(B) straight line

(C) ellipse

(D) circle

Sigma Percentile · Accepted Answer

### The Setup: A Dance of Fields

Imagine you are standing in a region of space where two fundamental forces of nature—the electric field $\mathbf{E}$ and the magnetic field $\mathbf{B}$—are perfectly aligned. They are parallel, pointing in the exact same direction, say, along the positive x-axis.

Now, we introduce a charged particle into this arena. We place it gently at the origin and release it from rest. The initial velocity $\mathbf{u}$ is exactly zero. What happens next is a beautiful demonstration of the Lorentz force.

### The Electric Push

The moment the particle is released, the electric field springs into action. Because the particle has a charge $q$, it experiences an electric force given by the equation $\mathbf{F}_e = q\mathbf{E}$.

Since the particle was initially at rest, this force gives it a sudden push. It begins to accelerate straight along the direction of the electric field. If the charge is positive, it moves in the direction of $\mathbf{E}$; if negative, it moves opposite to $\mathbf{E}$. Either way, it starts moving along that straight line.

### The Magnetic Silence

As the particle accelerates, it gains velocity $\mathbf{v}$. You might wonder, "Doesn't a moving charge experience a magnetic force?"

Let's look at the magnetic force equation: $\mathbf{F}_m = q(\mathbf{v} 	imes \mathbf{B})$. The magnitude of this force depends on the sine of the angle between the velocity vector and the magnetic field vector.

Because the particle was pushed by the electric field, its velocity $\mathbf{v}$ is perfectly parallel to $\mathbf{E}$. And since $\mathbf{E}$ is parallel to $\mathbf{B}$, the velocity $\mathbf{v}$ is also perfectly parallel to $\mathbf{B}$.

The angle between them is $0^\circ$. What is the sine of $0^\circ$? It is exactly zero! Therefore, the cross product vanishes, and the magnetic force $\mathbf{F}_m$ is absolutely zero.

### The Final Verdict

Throughout its journey, the magnetic field acts as a silent observer. It exerts no force to deflect the particle left, right, up, or down.

The particle is solely under the influence of the electric force, which continues to accelerate it along the same straight line. Thus, the path of the particle is a **straight line**.

This problem elegantly tests your understanding of vector cross products and the distinct ways electric and magnetic fields interact with matter. Always remember: a magnetic field can only deflect a charge if it cuts across the field lines!

Animated Solution for Physics - Magnetic Effects of Current: 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

Select Answer:

Visualized Solution

$Initial Setup$

$Electric Force$

$Velocity Acquired$

$Magnetic Force$

$Final Path$

$The Way Forward$

The Sigma Insight: Motion of a Charge in Magnetic Fields

The Setup

The Electric Push

The Magnetic Silence

The Final Verdict

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