Question:
Two parallel beams of protons moving in the same direction will:
Two parallel beams of protons moving in the same direction will:
Show Hint
Both the electric repulsion and the magnetic attraction act. The magnetic force is smaller by v squared over c squared, so the beams repel.
Updated On: Nov 13, 2026
attract each other
repel each other
be deflected normal to the plane containing the two beams
not interact with each other
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the question:
Two beams of protons travel in the same direction, side by side. Two kinds of force act between them, an electric one and a magnetic one.
Step 2: Electric force:
Protons carry the same charge, so each beam repels the other with an electric force.
Step 3: Magnetic force:
A moving beam of charges is an electric current. Parallel currents in the same direction attract each other. So the magnetic force is attractive.
Step 4: Compare the two forces:
For particles with speed \(v\) the ratio of the magnetic force to the electric force is \(\dfrac{F_m}{F_e} = \mu_0\epsilon_0 v^{2} = \dfrac{v^{2}}{c^{2}}\).
The speed \(v\) of the beam is far smaller than \(c\), so \(F_m \ll F_e\). The electric repulsion wins and the beams repel each other.
Step 5: Check the options:
(A) attract each other: only the weak magnetic force attracts, and it is beaten by the electric repulsion.
(B) repel each other: correct.
(C) deflected normal to the plane of the beams: the force between the beams acts in the plane of the two beams, along the line joining them.
(D) not interact: both forces exist, so they do interact.
Final Answer:
The beams repel each other. This is option (B).
Two beams of protons travel in the same direction, side by side. Two kinds of force act between them, an electric one and a magnetic one.
Step 2: Electric force:
Protons carry the same charge, so each beam repels the other with an electric force.
Step 3: Magnetic force:
A moving beam of charges is an electric current. Parallel currents in the same direction attract each other. So the magnetic force is attractive.
Step 4: Compare the two forces:
For particles with speed \(v\) the ratio of the magnetic force to the electric force is \(\dfrac{F_m}{F_e} = \mu_0\epsilon_0 v^{2} = \dfrac{v^{2}}{c^{2}}\).
The speed \(v\) of the beam is far smaller than \(c\), so \(F_m \ll F_e\). The electric repulsion wins and the beams repel each other.
Step 5: Check the options:
(A) attract each other: only the weak magnetic force attracts, and it is beaten by the electric repulsion.
(B) repel each other: correct.
(C) deflected normal to the plane of the beams: the force between the beams acts in the plane of the two beams, along the line joining them.
(D) not interact: both forces exist, so they do interact.
Final Answer:
The beams repel each other. This is option (B).
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