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Question

- x=3
- Magnetic field has a component along the z-direction
- Kinetic energy of the particle is constant
- x=−1.5

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Solution

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Under the influence of magnetic field only, speed and hence, kinetic energy remains constant.

So →F⋅→v=0⇒m→a⋅→v=0

⇒m(2^i+x^j)⋅(3^i+4^j)=0

⇒6+4x=0⇒x=−1.5

Let the magnetic field is →B=a^i+b^j+c^k, then from →F=q→v×→B

⇒m(2^i+x^j)=q(3^i+4^j)×(a^i+b^j+c^k)

⇒2m^i−1.5m^j=q(3b^k−3c^j−4a^k+4c^i)

4c=2m⇒c≠0

Hence, magnetic field has a component along z-direction.

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