A proton with a constant velocity passes through a region of space without any change in its velocity. If E and B represents the electric and magnetic field then the incorrect option is.
(a) 𝐸 = 0, 𝐵 = 0
(b) 𝐸 = 0, 𝐵 ≠ 0
(c) 𝐸 ≠ 0, 𝐵 = 0
(d) 𝐸 ≠ 0, 𝐵 ≠ 0
Parul SinglaTeacher
A proton with a constant velocity passes through a region of space without any change in its velocity
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The motion of a charged particle in electric and magnetic fields can be described by the Lorentz force equation:
\[ F = q(E + v \times B) \]
where:
\( F \) is the total force on the particle,
\( q \) is the charge of the particle,
\( E \) is the electric field,
\( B \) is the magnetic field, and
\( v \) is the velocity of the particle.
Given that the proton passes through a region of space without any change in velocity, its acceleration (\( a \)) is zero. Therefore, the net force (\( F \)) acting on it must be zero.
For the net force to be zero, either the electric field \( E \) or the magnetic field \( B \) or both must be zero.
Therefore, the correct option is the one that represents this condition.
(a) \( E = 0, \, B = 0 \) – This option implies that both electric and magnetic fields are zero. If this is the case, the net force on the proton will indeed be zero. This option is correct.
(b) \( E = 0, \, B \neq 0 \) – This option implies that the electric field is zero while the magnetic field is not zero. In this case, the net force on the proton could be non-zero due to the magnetic field. This option is incorrect.
(c) \( E \neq 0, \, B = 0 \) – This option implies that the electric field is not zero while the magnetic field is zero. In this case, the net force on the proton could be non-zero due to the electric field. This option is incorrect.
(d) \( E \neq 0, \, B \neq 0 \) – This option implies that both electric and magnetic fields are non-zero. In this case, the net force on the proton could be non-zero due to both fields. This option is incorrect.
Therefore, the incorrect option is (b) \( E = 0, \, B \neq 0 \).