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+3 votes
56.1k views
in Physics by (30.6k points)
closed by

In the product 

vector F = (v x B)

= qv x (Bi + Bj + B0k)

For q = 1 and v = 2i + 4j + 6k and

F = 4i - 20j + 12k

What will be the complete expression for B = ?

(1) - 8i - 8j - 6k 

(2) -6i -6j -8k 

(3) 8i + 8j - 6k 

(4) 6i + 6j - 8k

2 Answers

+1 vote
by (17.0k points)
selected by
 
Best answer

\(F = q(v \times B)\)

\(F.B = 0\)

\(v \times B = \hat i [4B_0 - 6B] + \hat j [6B - 2B_0] + \hat k [2B - 4B]\)

\(= \hat i [4B_0 - 6B] + \hat j (6B- 2B_0)-\hat k(2B)\)

\(4B_0 - 6B = 4\)     ......(1)

\(6B - 2B_0 = -20\)    ......(2)

\(-2B = 12\)    ......(3)

Solving (1), (2) and (3) we get

\(B = -6 \) and \(B_0 = - 8\)

\(\vec B = -6\hat i - 6\hat j - 8 \hat k\)

+4 votes
by (30.7k points)

Option : (2) -6i -6j -8k

vector F = q(v x B)

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