If a proton has velocity \((2\hat{i} + 3\hat{k})\) m/s and it is subjected to a magnetic field of \(4\hat{i}\) T, then its:
Since the magnetic force \(\vec{F} = q(\vec{v} \times \vec{B})\) is always perpendicular to the velocity, the work done is zero. Hence, the kinetic energy and speed remain constant.
A charge \( q = 1.6 \times 10^{-12} \text{ C} \) moving with speed of \( v \text{ m s}^{-1} \) crosses electric field \( |\vec{E}| = 6 \times 10^4 \text{ V m}^{-1} \) and magnetic field \( |\vec{B}| = 1.2 \text{ T} \). The electric field and magnetic fields are crossed and velocity \( v \) is also perpendicular to both. If the charge particle crosses both fields undeflected, the value of \( v \) is
For a particle to cross perpendicular electric and magnetic fields undeflected, the net force must be zero, which requires \( qE = qvB ⇒ v = \frac{E}{B} \). Substituting the given values: \( v = \frac{6 \times 10^4}{1.2} = 5 \times 10^4 \text{ m/s} \).
Consider the following statements:
A. Magnetic force on a moving charged particle is always non-zero.
B. Magnetic force can change kinetic energy of a charged particle.
C. Magnetic force can change linear momentum of a charged particle.
D. A charged particle at rest does not feel magnetic force on it.
The correct statement(s) is/are
Magnetic force is perpendicular to velocity, so it does no work and KE remains constant. It can change the direction of velocity (and thus momentum). For a particle at rest (\(v = 0\)), magnetic force is zero.
Assertion (A): A magnetic field can accelerate a charge particle.
Reason (R): A steady current carrying wire does not generate an electric field outside it.
In the light of the above statements, choose the correct answer from the options given below.
A magnetic field exerts a force perpendicular to velocity, changing its direction, hence accelerating the particle. Outside a steady current-carrying wire, there is no net charge, so the electric field is zero. Both statements are true, but they are unrelated.
In crossed electric and magnetic field, the velocity of charged particle which passes undeflected through the region may be (where \(E\) is electric field and \(B\) is magnetic field)
For a charged particle to pass undeflected in crossed fields, the electric force must balance the magnetic force: \(qE = qvB ⇒ v = \frac{E}{B}\).
A charged particle enters a magnetic field at right angles to the magnetic field. The field exists for a length equal to 1.5 times the radius of circular path of the circle. The particle will be deviated from its path by angle
Since the width of the magnetic field \(d = 1.5R > R\), the particle cannot cross the field to the other side. It will complete a semi-circular path inside the field and emerge from the same side it entered, yielding a deviation of \(180^\circ\).
In crossed electric and magnetic field, the velocity of charged particle which passes undeflected through the region may be (where \(E\) is electric field and \(B\) is magnetic field)
For a charged particle to pass undeflected in crossed electric and magnetic fields, the net Lorentz force must be zero. Hence, \(qE = qvB ⇒ v = \frac{E}{B}\).
A charged particle enters a magnetic field at right angles to the magnetic field. The field exists for a length equal to 1.5 times the radius of circular path of the circle. The particle will be deviated from its path by angle
Since the width of the magnetic field region \(x = 1.5R\) is greater than the radius \(R\), the particle will complete a semicircle inside the field and exit in the opposite direction, giving a deviation of \(180^\circ\).
Assertion (A): Magnetic force between two charge is generally much smaller than the electric force between them.
Reason (R): Speeds of charges are much smaller than the free-space speed of light.
Magnetic force \(F_m = qvB\) and electric force \(F_e = qE\). For moving charges, \(B = \frac{v}{c^2}E\). Thus, \(F_m = \frac{v^2}{c^2}F_e\). Since speeds \(v\) of charges are much smaller than the speed of light \(c\), \(F_m\) is much smaller than \(F_e\). Both (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): The nature of electromagnetic force acting on a moving charged particle in external magnetic field is frame dependent.
Reason (R): The force acting on a charged particle always varies with shift of frame.
Assertion (A) is false because the total electromagnetic force is invariant under Lorentz transformations, meaning its nature is not frame dependent. Reason (R) is also false; while the magnetic force itself varies with frame, the total electromagnetic force remains invariant. Therefore, both assertion and reason are false.