In the productF-q v-B-qv- B-B-B0k-For q - 1 and v- 2-4-6k-F-4-20-12k-What will be the complete expression for B-

Given: q = 1 v= 2î+4ĵ+6k̂ nbsp; B=Bî+Bĵ+B_0k̂ nbsp; nbsp; F=4î 20ĵ+12k̂ Now, F=q(v×B) ⇒ nbsp; 4î 20ĵ+12k̂=1 [(2î+4ĵ+6k̂)×(Bî+Bĵ+B_0k̂)] ⇒ nbsp; 4 ...

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Byju's Answer

Standard XII

Physics

Work Done as Dot Product

In the produc...

Question

In the product

$\to F = q (\to v \times \to B) = q \to v \times (B^i + B^j + B_{0}^k)$

For $q = 1$ and $\to v = 2^i + 4^j + 6^k$ ,
$\to F = 4^i - 20^j + 12^k$

What will be the complete expression for $\to B$ ?

6^i + 6^j - 8^k

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- 8^i - 8^j - 6^k

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- 6^i - 6^j - 8^k

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8^i + 8^j - 6^k

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Solution

The correct option is C $- 6^i - 6^j - 8^k$
Given:

$q = 1$
$\to v = 2^i + 4^j + 6^k$
$\to B = B^i + B^j + B_{0}^k$
$\to F = 4^i - 20^j + 12^k$

Now,

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

$\Rightarrow 4^i - 20^j + 12^k = 1 [(2^i + 4^j + 6^k) \times (B^i + B^j + B_{0}^k)]$

$\Rightarrow 4^i - 20^j + 12^k = (4 B_{0} - 6 B)^i - (2 B_{0} - 6 B)^j + (- 2 B)^k$

On comparing and solving, we get,

$B = - 6$ and $B_{0} = - 8$

Therefore,

$\to B = B^i + B^j + B_{0}^k = - 6^i - 6^j - 8^k$

Hence, option $(C)$ is the correct answer.

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In the product →F=q(→v×→B)=q→v×(B^i+B^j+B0^k) For q=1 and →v=2^i+4^j+6^k, →F=4^i−20^j+12^k What will be the complete expression for →B?

In the product

$\to F = q (\to v \times \to B) = q \to v \times (B^i + B^j + B_{0}^k)$

For $q = 1$ and $\to v = 2^i + 4^j + 6^k$ ,
$\to F = 4^i - 20^j + 12^k$

What will be the complete expression for $\to B$ ?