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Question

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?
  1. If y>x, the force will act along y-axis
  2. No force will act on charged particle if x=y
  3. If x>y,F(x2y2)
  4. 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(x2y2)^k

If x=y, f=q(x2y2)=q(00)=0

If x>y, f=q(x2y2)^k>0

If y>x, f=q(x2y2)^k<0 and it points in the vez axis.

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