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`         The force on a charged particle due to electric and magnetic fields is given by F ⃗=qE ⃗+qv×B ⃗ . Suppose E ⃗ is  along the X-axis and B ⃗ along the Y-axis. In what direction and with what minimum speed v should a positively charged particle be sent so that the net force on it is zero ?`
3 years ago

Kevin Nash
332 Points
```										18. 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°) as shown in the
figure, so that the force is zero.

```
3 years ago
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