JEE Main On 8 April 2017 Question 29
Question: In a certain region static electric and magentic fields exist. The magnetic field is given by $ \vec{B}=B _0( \hat{i}+2\hat{j}-4\hat{k} ). $ If a test charge moving with a velocity $ \vec{\upsilon }={\upsilon_0}( 3\hat{i}-\hat{j}+2\hat{k} ) $ experience no force in that region, then the electric field in the region, in SI units, is - [JEE Online 08-04-2017]
Options:
A) $ \vec{E}=-{\upsilon_0}B _0( \hat{i}+\hat{j}+7\hat{k} ) $
B) $ \vec{E}=-{\upsilon_0}B _0( 3\hat{i}-2\hat{j}-4\hat{k} ) $
C) $ \vec{E}={\upsilon_0}B _0( 14\hat{i}+7\hat{k} ) $
D) $ \vec{E}=-{\upsilon_0}B _0( 14\hat{j}+7\hat{k} ) $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ F _{e}=F _{n}=0 $ $ F _{e}=-F _{m} $ $ =-q( \vec{v}\times \vec{B} ) $ $ =-{\upsilon_0}B _0[ ( 3\hat{i}-\hat{j}+2\hat{k} )\times ( \hat{i}+2\hat{j}-4\hat{k} ) ] $ $ =-{\upsilon_0}B _0( 14\hat{i}+7\hat{k} ) $
