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Chapter 27: Problem 47

Two protons are moving with same velocity in magnetic field of same magnitude, then : (a) magnetic force on protons may be zero (b) magnetic force on both must be same to each other (c) magnetic force on both may or may not be same to each other (d) both (a) and (c) are correct

Short Answer

Expert verified
The correct option is (d) both (a) and (c) are correct.

Step by step solution

01

Understanding the Magnetic Force Formula

The magnetic force exerted on a moving charge in a magnetic field is given by the formula \( F = qvB \sin(\theta) \), where \( F \) is the magnetic force, \( q \) is the charge of the particle, \( v \) is the velocity of the particle, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the velocity vector and the magnetic field direction.
02

Analyzing the Given Conditions

Both protons have the same charge, \( q \), and are moving with the same velocity, \( v \). They are also in a magnetic field of the same magnitude, \( B \). Thus, the only variable that can change the force experienced by each proton is the angle \( \theta \) between their velocity vector and the magnetic field.
03

Evaluating Option (a)

For the magnetic force to be zero, \( \sin(\theta) = 0 \) must be true. This occurs when \( \theta = 0^\circ \) or \( 180^\circ \), meaning the velocity vector is parallel or antiparallel to the magnetic field. Therefore, it is possible for the magnetic force on the protons to be zero.
04

Evaluating Option (b)

The force will be the same if both protons have the same \( \theta \) value, resulting in identical \( \sin(\theta) \) values. This is not guaranteed as the orientation of their velocity concerning the field could be different.
05

Evaluating Option (c)

The forces may or may not be the same, as it depends on \( \theta \) value for each proton. Different angles will result in different forces due to the \( \sin(\theta) \) component.
06

Combining Observations and Choosing the Correct Answer

From the analysis: (a) is possible due to \( \theta = 0 \) or \( 180^\circ \), (b) isn't guaranteed unless \( \theta \) is identical, (c) is also valid as \( \theta \) could vary, making (d) 'both (a) and (c) are correct' the best choice.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Proton Motion
In physics, a proton is a positively charged particle found in the nucleus of an atom. Understanding proton motion is essential in various scientific areas, including nuclear physics and electromagnetism.
When protons move, they can generate magnetic fields if unbalanced forces act on them. Because protons carry a positive charge, their motion is influenced by electromagnetic fields, much like how a balloon will drift in the wind. This interaction is significant when protons travel through a magnetic field.
  • Protons have a positive electrical charge, which affects how they interact with fields around them.
  • Their mass is about 1836 times that of electrons, influencing how much force is needed to change their motion.
  • In a magnetic field, the direction and speed of proton movement are crucial for determining how much force they experience.
By mastering the basics of proton motion, students can better comprehend how particles interact in magnetic environments.
Magnetic Field
A magnetic field is an invisible force exerted by magnets or moving charges, affecting certain materials within its scope. This concept is central to understanding many natural phenomena and technological applications, from compass use to MRI machines.
In essence, a magnetic field can be visualized by imagining lines of magnetic force bubbling outwards from the pole of a magnet. The strength and direction of these forces are key to interpreting how objects like protons will move within the field.
  • Magnetic fields are vector fields, meaning they have both magnitude and direction.
  • The unit of measurement for the magnetic field strength is the Tesla (T).
  • Magnetic fields can cause charged particles like protons to follow curved paths, rather than moving in straight lines.
Varying magnetic field strengths will contribute differently to the force exerted on other objects present.
Charge-Velocity Interaction
The interaction between a charged particle's velocity and a magnetic field generates a magnetic force. This is governed by the equation: \[ F = qvB \sin(\theta) \] where:
  • \( F \) is the magnetic force.
  • \( q \) represents the charge of the particle.
  • \( v \) is the velocity at which the particle is moving.
  • \( B \) denotes the magnetic field strength.
  • \( \theta \) is the angle between the particle's velocity vector and the magnetic field direction.
For practical understanding:- If \( \theta \) is 0 or 180 degrees, the force \( F \) becomes zero, since \( \sin(\theta) = 0 \).- When \( \theta \) is 90 degrees, \( \sin(\theta) = 1 \), leading to maximum force exertion.This principle highlights that the effect of a magnetic field on a moving charge is not just determined by their individual strengths but by their orientation relative to each other.

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Most popular questions from this chapter

A conducting loop carrying a current is placed in a non-uniform magnetic field perpendicular to the plane of loop. Then : (a) loop must experience force (b) loop may experience torque (c) loop must experience torque (d) none of the above

A charged particle of mass \(m\) and charge \(q\) is accelerated through a potential difference of \(V\) volt. It enters a region of uniform magnetic field which is directed perpendicular to the direction of motion of the particie. The particle will move on a circular path of radius given by: (a) \(\sqrt{\left(\frac{V m}{q B^{2}}\right)}\) (b) \(\frac{2 V m}{q B^{2}}\) (c) \(\sqrt{\left(\frac{2 V_{m}}{q}\right)}\left(\frac{1}{B}\right)\) (d) \(\sqrt{\left(\frac{V m}{q}\right)}\left(\frac{1}{B}\right)\)

A coil carrying electric current is placed in uniform magnetic field. Then: (a) torque is formed (b) emf is induced (c) both (a) and (b) are correct (d) none of the above.

A long copper wire carries current in the east direction. The electrons are moving with a drift velocity \(\overrightarrow{\mathbf{u}}\). An. observer now moves with the velocity \(\overrightarrow{\mathbf{u}}\). In the frame of this observer: (a) electric field is present (b) magnetic field due to wire is zero (c) only magnetic field is present (d) none of the above

Two thin long parallel wires separated by a distance \(b\) are carrying a current \(I\) amp each. The magnitude of the force per unit length exerted by one wire on the other is : (a) \(\frac{\mu_{0} I^{2}}{b^{2}}\) (b) \(\frac{\mu_{0} l^{2}}{2 \pi b}\) (c) \(\frac{\mu_{0} I}{2 \pi b}\) (d) \(\frac{\mu_{0} l}{2 \pi b^{2}}\)
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