1. -8i-8j-6k 2. -6i-6j-8k 3. 8i+8j-6k 4. 6i+6j-8k

Answer: 2. -6i-6j-8k Key idea: expand vec v×vec B as a determinant and match components. Here vec v=(2,4,6) , vec B=(B_x,B_y,B_z) , vec F=(4,-20,12) . x: 4B_z-6B_y=4 y: 6B_x-2B_z=-20 z: 2B_y-4B_x=12 The stem has B_x=B_y . Then z gives -2B_x=12 , so B_x=B_y=-6 . From x: 4B_z+36=4⇒ B_z=-8 . Check y: -36+16=-20 . So vec B=-6hat i-6hat j-8hat k . Option 2.

Topic: Force on moving charge in magnetic and electric fields· Magnetic Effects of Current and Magnetism

In the productF = q(v×B) = q v×(Bi+Bj+B_0k)For q = 1 and v = 2i+4j+6k and F = 4i-20j+12kWhat will be the complete expression for B ?

1. \(-8\hat{i}-8\hat{j}-6\hat{k}\)

2. \(-6\hat{i}-6\hat{j}-8\hat{k}\)

3. \(8\hat{i}+8\hat{j}-6\hat{k}\)

4. \(6\hat{i}+6\hat{j}-8\hat{k}\)

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Answer: 2. \(-6\hat{i}-6\hat{j}-8\hat{k}\)

Key idea: expand \(\vec v\times\vec B\) as a determinant and match components. Here \(\vec v=(2,4,6)\), \(\vec B=(B_x,B_y,B_z)\), \(\vec F=(4,-20,12)\).

x: \(4B_z-6B_y=4\)
y: \(6B_x-2B_z=-20\)
z: \(2B_y-4B_x=12\)

The stem has \(B_x=B_y\). Then z gives \(-2B_x=12\), so \(B_x=B_y=-6\). From x: \(4B_z+36=4\Rightarrow B_z=-8\). Check y: \(-36+16=-20\). So \(\vec B=-6\hat i-6\hat j-8\hat k\). Option 2.

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In the productF = q(v×B) = q v×(Bi+Bj+B_0k)For q = 1 and v = 2i+4j+6k and F = 4i-20j+12kWhat will be the complete expression for B ?

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