When a proton is released from rest in a room, it starts with an initial acceleration `a_(0)` towards west. When it is projected towards north with a speed `v_(0)` it moves with an initial accelaration `3a_(0)` towards west. The electric and the maximum possible magnetic field in the room
(i) `(ma_(0))/(e)`, towards west
(ii) `(2 ma_(0))/(ev_(0))`, downward
(iii) `(ma_(0))/(e)`, towards east
(iv) `(2ma_(0))/(ev_(0))`, upward

Explanation

Since acceleration is towards west and charge on proton is `+ve` i.e electric field is acting along west
Electric force `F_(e) = eE = ma_(0) rArr E = (ma_(0))/(e)`
When proton is projected towards north with speed `v_(0)`, magnetic force also acts. Since total acceleration is `3a_(0)` towards west i.e. acceleration `2a_(0)` is due to magnetic force. Magnetic force is along west. Since velocity is along north, force along west i.e. magnetic field is inside the plane of paper.
`F_(m) = Be v_(0) sin 90^(@) = B e v_(0) = 2 ma_(0)`
`B = (2ma_(0))/(ev_(0)), ox`