Question

In a region of a uniform electric field `vec E`, a negatively charged particle is moving with a constant velocity `vec v = -v_0 hat i` near a long straight conductor coinciding with XX' axis and carrying current I towards −X axis. The particle remains at a distance d from the conductor.

1. Draw diagram showing direction of electric and magnetic fields.
2. What are the various forces acting on the charged particle?
3. Find the value of v_o in terms of E, d and I.

Answer 1

i. The graphical ray diagram illustrating the directions of velocity, electric field, and magnetic field.

Electric and Magnetic Field Directions:

ii. The forces acting on the charged particle include:

• Electric Force: F_E = q_E, where q is the charge of the particle.
• Magnetic Force (Lorentz Force): F_B = `q(vec v xx vec B)`, where B is the magnetic field due to the conductor.
• Gravitational Force: F_G = mg, where m is the mass of the particle.

iii. The magnetic field due to the conductor at a distance d is given by:

B = `mu_0 I/(2 pi)`

The Lorentz force acting on the charged particle:

qv₀B = qE

`(V_0 mu_0 I)/(2 pi d)` = E

Solving for V₀:

V₀ = `(2 pi d E)/(mu_0I)`