Exams › GATE › Technical

A uniform and constant magnetic field B = 2B in exists in the z direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity v = vₓ x̂ + v_z ẑ. Given that B, m, q, vₓ and v_z are all non-zero, which one of the following describes the eventual trajectory of the particle?

1. Helical motion in the z direction.
2. Circular motion in the xy plane.
3. Linear motion in the z direction.
4. Linear motion in the x direction.

Correct answer: Helical motion in the z direction.

Solution

The particle experiences a magnetic force due to its velocity in the presence of the magnetic field, which causes it to move in a circular path in the xy plane while simultaneously moving along the z direction due to its initial velocity component in that direction, resulting in a helical trajectory.

Related GATE Technical questions

• In the circuit shown below, V_S is a constant voltage source and I_L is a constant current load. The value of I_L that maximizes the power absorbed by the constant current load is
• The Ebers-Moll model of a BJT is valid
• A long-channel NMOS transistor is biased in the linear region with VDS=50 mV and is used as a resistance. Which one of the following statements is NOT correct?
• The number and direction of encirclements around the point -1 + j0 in the complex plane by the Nyquist plot of G(s) = (1-s)/(4+2s) is
• The three-dimensional state of stress at a point is given by σ = [[10, 0, 0],[0, 40, 0],[0, 0, 0]] MPa. The maximum shear stress at the point is
• A 2 m wide strip footing is founded at a depth of 1.5 m below the ground level in a homogeneous pure clay bed. The clay bed has unit cohesion of 40 kPa. Due to seasonal fluctuations of water table from peak summer to peak monsoon period, the net ultimate bearing capacity of the footing, as per Terzaghi’s theory, will

⚔️ Practice GATE Technical free + battle 1v1 →