A charge particle is moving in a uniform magnetic field (2 î+3 ĵ) T. If it has an acceleration of (α î-4 ĵ) m / s², then the value of α will be :

Solution

Physics sir · 3 steps

Magnetic force is always perpendicular to B, so set the dot product of a and B to zero.

1. Direction of force. The magnetic force is F⃗ = q v⃗ × B⃗. A cross product is always perpendicular to both vectors in it, so F⃗ is perpendicular to B⃗.
2. Same for acceleration. Acceleration is a⃗ = F⃗/m, so it points along F⃗. That means a⃗ is also perpendicular to B⃗, and their dot product must be zero.

   a⃗·B⃗ = (α)(2) + (-4)(3) = 2α - 12 = 0

3. So. 2α = 12, which gives α = 6. The answer is (b).

The idea to keep. A magnetic field can only push sideways. Whenever B is given along with the force or acceleration of a charge, set their dot product to zero.

Answer from the NTA final answer key. Solution by PrepWiser.