### Neet Solved Paper 2013 Question 28

##### Question: 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 $ {\upsilon_0} $ it moves with an initial acceleration $ 3a _0 $ towards west. The electric and magnetic fields in the room are

#### Options:

A) $ \frac{ma _0}{e}west,\frac{2ma _0}{ev _0}up $

B) $ \frac{ma _0}{e}west,\frac{2ma _0}{ev _0}dwon $

C) $ \frac{ma _0}{e}east,\frac{3ma _0}{ev _0}up $

D) $ \frac{ma _0}{e}east,\frac{3ma _0}{ev _0}down $

## Show Answer

#### Answer:

Correct Answer: B

#### Solution:

- Initial acceleration, $ a _0=\frac{eE}{m} $ ?(i)

$ \Rightarrow $ $ E=\frac{a _0m}{e}\therefore \frac{ev _0B+eE}{m}=3a _0 $ Or $ ev _0B+eE=3a _0m $

$ \therefore $ $ ev _0B=3ma _0-eE $

$ \Rightarrow $ $ =3ma _0-ma _0 $ [from eq. (1)]

$ \Rightarrow $ $ ev _0B=2ma _0 $

$ \therefore $ $ B=\frac{2ma _0}{ev _0} $