In a certain region static electric and magnetic fields exist. The magnetic field is given by `vec(B) = B_(0) (hat(i) + 2hat(j)-4hat(k))`. If a test charge moving with a velocity, `vec(upsilon) = upsilon_(0)(3hat(i)-hat(j) +2hat(k))` experience no force in that region, then the electric field in the region, in SI units, is-

Options

A. `vec E = - v_(0) B_(0)(3 hat I - 2 hat j - 4 hat k)`
B. `vecE = - v_(0) B_(0) ( hat I + hat j + 7 hat k) `
C. `vecE = v_(0)B_(0) ( 14 hat j + 7 hat k)`
D. `vec E = - v_(0) B_(0) *14 hat j + 7 hat k)`

Answer

D

Explanation

Resultant of electric and magnetic force should be zero. Hence we can write the following:
`vecF_(e) + vecF_(m) = 0 `
`rArr vecF_(e) = - vecF_(m)`
`rArr qvecE = - q vecv xx vecB`
`rArr vecE = vecB xx vec v`
`rArr vecE = B_(0) [( hat i + 2hat j- 4 hat k) xx v_(0) (3 hat i - hat j + 2hat k)]`
`rArr vecE = B_(0)v_(0)[( hat i + 2hat j - 4 hat k) xx (3 hat i - hat j + 2hat k)]`
`rArr vecE = - B_(0)v_(0)(14 hat j + 7 hat k)`