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 \(180^\circ\).
The relative permeability of a ferromagnetic material is \( 5999 \). Its magnetic susceptibility is
The relation between relative permeability and magnetic susceptibility is \( \mu_r = 1 + \chi_m \). Therefore, \( \chi_m = \mu_r - 1 = 5999 - 1 = 5998 \).
Assertion (A): Pole pieces of the magnet used in a moving coil galvanometer are given a concave shape to achieve a radial magnetic field.
Reason (R): A radial magnetic field ensures a better current sensitivity and also makes possible to use a linear scale for current measurement.
Concave pole pieces ensure a radial magnetic field in a moving coil galvanometer, keeping \(\vec{B}\) always perpendicular to the coil's area vector. This ensures maximum torque \(\tau = NIAB\) and a linear scale (deflection \(\phi \propto I\)), leading to better current sensitivity. Both (A) and (R) are true, and (R) explains (A).
Assertion (A): Parallel current in wires attracts to each other due to magnetic force.
Reason (R): Two electron beams moving parallel to each other repels to each other due to electric force.
Wires with parallel currents attract due to magnetic force, so (A) is true. Two parallel electron beams experience electric repulsion due to like charges, so (R) is true. However, the magnetic force (A) and electric force (R) are distinct phenomena. Thus, (R) does not explain (A).
Assertion (A): Two long parallel conductors carrying currents in the same direction experience a force of attraction.
Reason (R): The magnetic fields produced in the space between two long parallel current carrying conductors (by each of these conductors) are in the same direction.
Parallel currents in the same direction attract, so (A) is true. For two parallel currents in the same direction, the magnetic fields in the space between them are in opposite directions (e.g., one into the page, one out of the page by Right Hand Rule). Therefore, (R) is false.
Assertion (A): Force on a current carrying wire of length \(dvec{l}\) placed in magnetic field \(vec{B}\) is given by \(d\vec{F} = Id\vec{l} \times \vec{B}\).
Reason (R): Net force on a current carrying loop in a non-uniform magnetic field must be non-zero.
The Lorentz force law states \(d\vec{F} = I(d\vec{l} \times \vec{B})\), so (A) is true. For a loop in a uniform field, net force is zero; in a non-uniform field, it is generally non-zero, so (R) is true. However, (R) is a consequence of the force law, not an explanation of the force law itself.
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.
Assertion (A): When a straight wire carrying current is placed along the axis of a current carrying ring, it starts rotating about the wire.
Reason (R): Charged ring will experience a torque when current carrying cable will pass through its axis.
Assertion (A) is false. A straight wire carrying current along the axis of a ring produces a magnetic field that is perpendicular to the current elements of the ring. Consequently, the magnetic force \(I(\vec{dl} \times \vec{B}))\ on each element is zero, resulting in no net force or torque on the ring.
Reason (R) is also false because no torque is experienced under these conditions. Both assertion and reason are false.