Question

. The force on a charged particle due to electric and
magnetic fields is given by F= q E +qux B. Suppose
E is along the X-axis and B along the Y-axis. In what
direction and with what minimum speed u should a
positively charged particle be sent so that the net force
on it is zero ?​

Answer 1

Answer:

Give F ⃗ qE ⃗ q(v ⃗ B ⃗) = 0

⇒ E ⃗ (v ⃗ B ⃗) So, the direction of v ⃗ x B ⃗ should be opposite to the direction of E ⃗ . Hence, v ⃗ should be in the positive yz-plane.

Again, E = vB sin θ

⇒ v = E/(B sin⁡θ ) For v to be minimum, θ = 90° and so Vmin = F/B So, the particle must be projected at a minimum speed of E/B along +ve z-axis (θ = 90°).