A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B represent the electric and magnetic fields respectively. Then, this region of space may have
- E = 0, B = 0
- E= 0, B $\ne$ 0
- E $\ne$ 0, B = 0
- E $\ne$ 0, B $\ne$ 0
The Correct Option is D
Approach Solution - 1
If both E and B are zero, then \(F_e\) and \(F_m\) both are zero.
Hence, velocity may remain constant. Therefore, option (a) is correct.
If E = 0, B \(\ne\) 0 but velocity is parallel or antiparallel to magnetic field, then also \(F_e and F_m\) both are zero. Hence, option (b) is also correct.
If \(E \ne 0, 5 \ne 0 \ but\ F_e + F_m = 0,\) then also velocity may remain constant or option (d) is also correct.
Approach Solution -2
If there's no electric field (E) and no magnetic field (B), then both the electric force (Fe) and the magnetic force (Fm) are zero. This means the velocity of the object can stay the same. So, option (a) is right.
If there's no electric field (E = 0), but there is a magnetic field (B ≠ 0), and the velocity is either parallel or antiparallel to the magnetic field, then both Fe and Fm are zero. Therefore, option (b) is also correct.
If there's both an electric field (E ≠ 0) and a magnetic field (B ≠ 0), but the sum of Fe and Fm is zero, then the velocity can stay constant, so option (d) is also correct.
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Concepts Used:
Moving Charges and Magnetism
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Magnetism:
- The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
- And Magnetism is a property that is displayed by Magnets and produced by moving charges, which results in objects being attracted or pushed away.
Magnetic Field:
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.
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