Question 56: Magnetism and Matter

Question

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

Accepted Answer

For this scenario, it's important to recall how magnetic fields influence the motion of charged particles, and the configuration of the magnetic field within a solenoid. Inside a long solenoid, the magnetic field lines run parallel to the axis of the solenoid. The strength of this field is uniform and depends on the current running through the solenoid's coils and the number of turns per unit length but is independent of the position inside the solenoid as long as one is sufficiently far from the ends.
The force experienced by a charged particle moving in a magnetic field is given by the Lorentz force equation: $$\vec{F} = q(\vec{v} 	imes \vec{B})$$ where
$$q$$ is the charge of the particle,
$$\vec{v}$$ is the velocity of the particle, and
$$\vec{B}$$ is the magnetic field.
For an electron moving along the axis inside a solenoid:
The magnetic field ($$\vec{B}$$) inside the solenoid is parallel to the axis of the solenoid.
The velocity of the electron ($$\vec{v}$$) is also parallel to the axis of the solenoid and hence parallel to $$\vec{B}$$.
Since the cross product of two parallel vectors (in this case, $$\vec{v}$$ and $$\vec{B}$$) is zero, the Lorentz force ($$\vec{F} = q(\vec{v} 	imes \vec{B})$$) acting on the electron will be zero. Therefore, the electron will not experience any force due to the magnetic field of the solenoid, as there is no component of its velocity that is perpendicular to the magnetic field within the solenoid.
Given the above explanation, the correct option is:
Option D: the electron will continue to move with uniform velocity along the axis of the solenoid.
This is because, in the absence of any force acting on it, the electron will maintain its state of motion according to Newton's first law of motion, which states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

Answer

the electron will experience a force at $$45^{\circ}$$ to the axis and execute a helical path.

Answer

the electron will be accelerated along the axis.

Answer

the electron path will be circular about the axis.

Answer

the electron will continue to move with uniform velocity along the axis of the solenoid.

Magnetism and Matter

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

Choose the correct answer: