There are unifonn electric and magnetic fields in a region pointing along X-axis. An α-particle is projected along Y-axis with a velocity v. The shape of the trajectory will be :
The correct answer is (C) Helical with its axis parallel to X-axis.
The electric field exerts a force along the X-axis, while the magnetic field causes circular motion in the YZ plane. The superposition of linear and circular motions results in a helical trajectory.
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An α-particle projected along the Y-axis with velocity
v in the presence of uniform electric and magnetic fields along the X-axis experiences a magnetic force perpendicular to both velocity and magnetic field, causing circular motion in the YZ plane. The electric field imparts acceleration along the X-axis, resulting in a helical trajectory with its axis parallel to the X-axis.
Answer: (C) Helical with its axis parallel to X-axis.
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The magnetic field at the common center due to a current-carrying loop is given by:
B = μ0I/2R
Let the currents in loops P and Q be Ip and = Iq = 9A, with radii Rp and Rq
such that Rp/Rq = 2/3. For zero net magnetic field:
Ip/Iq = Rq/Rp = 3/2 ⟹ Ip = 6A To cancel Q’s anticlockwise field,
P must carry 6 A in the clockwise direction.
Answer: (D) 6 A in the clockwise direction.
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