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# A charged particle with velocity →v=x^i+y^j moves in a magnetic field →B=y^i+x^j. The force acting on the particle has magnitude F. Which one of the following statements is/are correct?If y>x, the force will act along y-axisNo force will act on charged particle if x=yIf x>y,F∝(x2−y2)If x>y, the force will act along z-axis

A
No force will act on charged particle if x=y
B
If x>y,F(x2y2)
C
If x>y, the force will act along z-axis
D
If y>x, the force will act along y-axis
Solution
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#### →v=x^i+y^j→B=y^i+x^j→f=q(→v×→B)=q((x^i+y^j)×(y^i+x^j))=q(x2−y2)^kIf x=y, →f=q(x2−y2)=q(0−0)=0If x>y, →f=q(x2−y2)^k>0If y>x, →f=q(x2−y2)^k<0 and it points in the −vez− axis.

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