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A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

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Yes, because magnetic force can change the direction of v, not its magnitude.
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NCERT GUJARATI-MOVING CHARGES AND MAGNETISM -ADDITIONAL EXERCISES
  1. Two concentric circular coils X and Y of radii 16 cm and 10 cm, respec...

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  2. A magnetic field of 100 G (1 G = 10^(-4) T) is required which is unifo...

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  3. For a circular coil of radius R and N turns carrying current I, the ma...

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  4. A toroid has a core (non-ferromagnetic) of inner radius 25 cm and oute...

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  5. A magnetic field that varies in magnitude from point to point but has ...

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  6. A charged particle enters an environment of a strong and non-uniform m...

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  7. An electron travelling west to east enters a chamber having a uniform ...

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  8. An electron emitted by a heated cathode and accelerated through a pote...

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  9. A magnetic field set up using Helmholtz coils (described in Exercise 4...

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  10. A straight horizontal conducting rod of length 0.45 m and mass 60 g is...

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  11. The wires which connect the battery of an automobile to its starting m...

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  12. A uniform magnetic field of 1.5 T exists in a cylindrical region of ra...

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  13. A uniform magnetic field of 0.3 T is established along the positive Z-...

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  14. A circular coil of 20 turns and radius 10 cm is placed in a uniform ma...

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  15. A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of...

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  16. A galvanometer coil has a resistance of 12 Omega and the metre shows...

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  17. A galvanometer coil has a resistance of 15 Omega and the metre shows ...

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