Question

A proton with speed v perpendicular to a magnetic field B is experiences a force F. if the speed of the proton is doubled, the new force is
a) F/2
b) F
c) 2F
d) 4F

Answer 1

Answer on Question 51523, Physics, Electromagnetism

Question:

A proton with speed $v$ perpendicular to a magnetic field $B$ is experiences a force $F$. If the speed of the proton is doubled, the new force is

a) $F / 2$

b) $F$

c) $2F$

d) $4F$

Solution:

The force that acts on the proton when it moves with speed $v$ perpendicular to a magnetic field $B$ looks like:

$$F = q v \times B,$$

where $F$ is the force that acts on the proton, $q$ is the charge of the proton, $v$ is the proton speed and $B$ is the magnetic field.

Then, from the condition of the question we know that the speed of the proton is doubled, so it will be $2v$. Taking into account, that $q$ and $B$ is constant we get that the force is proportional to the speed of the proton:

$$2F = 2v$$

Answer:

c) $2F$

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