Question 68: Magnetism and Matter

Question

An electron is moving along the positive $$\mathrm{x}$$-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then
A. The electron will experience magnetic force along positive y-axis
B. The electron will experience magnetic force along negative y-axis
C. The electron will not experience any force in magnetic field
D. The electron will continue to move along the positive $$\mathrm{x}$$-axis
E. The electron will move along circular path in magnetic field
Choose the correct answer from the options given below:

Accepted Answer

The Lorentz force equation is given as:
$$\vec{F} = -q(\vec{v} 	imes \vec{B})$$
The electron is moving along the positive x-axis, so its velocity vector is $$\vec{v} = v_x \hat{i}$$. The magnetic field is applied parallel to the negative z-axis, so its magnetic field vector is $$\vec{B} = -B_z \hat{k}$$.
Now, we can calculate the cross product of the velocity and magnetic field vectors:
$$\vec{v} 	imes \vec{B} = (v_x \hat{i}) 	imes (-B_z \hat{k})$$
Using the cross product properties, we get:
$$\vec{v} 	imes \vec{B} = -v_x B_z (\hat{i} 	imes \hat{k})$$
The cross product of $$\hat{i}$$ and $$\hat{k}$$ is $$-\hat{j}$$, so:
$$\vec{v} 	imes \vec{B} = -v_x B_z (-\hat{j}) = v_x B_z \hat{j}$$
Since the electron has a negative charge, the magnetic force will be in the opposite direction:
$$\vec{F} = -(-e)(v_x B_z \hat{j}) = e(v_x B_z \hat{j})$$
As a result, the electron will experience a magnetic force along the negative y-axis.
Additionally, as mentioned earlier, when a charged particle moves through a magnetic field perpendicular to its velocity, it follows a circular path. In this case, the velocity of the electron is along the positive x-axis, and the magnetic field is along the negative z-axis, which are indeed perpendicular to each other. As a result, the electron will move along a circular path in the magnetic field.
Hence, the correct answer is:
(C) B and E only

Answer

A and E only

Answer

B and D only

Answer

B and E only

Answer

C and D only

Magnetism and Matter

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