Magnetic field due to currentHard

Question

A proton moving with a constant velocity passes through a region of space without any change in its velocitiy. If E and B represent the electric and magetic fields respectively. Then, this region of space may have

Options

A.E = 0, B = 0
B.E = 0, B ≠ 0
C.E ≠ 0, B = 0
D.E ≠ 0, B ≠ 0

Solution

If both E and B are zero, then and both are zero.
Hence, velocity may remain constant. Therefore, option (a) is correct.
If E = 0, B ≠ 0 0 but velocity is parallel or antiparallel to magnetic field, then also and both are zero. Hence option (b) is correct.
If E ≠ 0, B ≠ 0 but + = 0, then also velocity may remain constant or option (d) is also correct.

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