When a proton is released from rest in a room, it has an initial acceleration a₀ towards the west. When it is projected towards the north with speed v₀, its initial acceleration is 3a₀ towards the west. Find the directions and magnitudes of the electric and magnetic fields in the room.
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Question

When a proton is released from rest in a room, it has an initial acceleration a₀ towards the west. When it is projected towards the north with speed v₀, its initial acceleration is 3a₀ towards the west. Find the directions and magnitudes of the electric and magnetic fields in the room.

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G1 Physics · Accepted Answer

Step 1: When the proton starts from rest, magnetic force q(v⃗ × B⃗) is zero. Electric force must therefore satisfy eE = ma₀. Step 2: Therefore E = ma₀/e, directed west (same direction as acceleration of a positive charge). Step 3: When projected north at speed v₀, net westward force is 3ma₀. Electric force already contributes ma₀ west, so the additional magnetic force is 2ma₀ west. Step 4: e v₀ B = 2ma₀, giving B = 2ma₀/(ev₀). Step 5: With v⃗ north, v⃗ × B⃗ points west only when B⃗ points down.…