A uniform electric field E is present horizontally along the paper throughout region but uniform magnetic field B0 is present horizontally (perpendicular to plane of paper in inward direction) right to the line AB as shown. A charge particle having charge q and mass m is projected vertically upward and crosses the line AB after time t0. The speed of projection if particle moves after t0 with constant velocity. (given qE = mg) is nto. Find the value of ‘n’. (g = 9.8 m/s2)

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answer is 00019.60.

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Detailed Solution

When crosses ABqvB0cos⁡θ=mgqvB0sin⁡θ=qEtan⁡θ=qEmg=1θ=π4 along horizontal vcos⁡θ=qEmt0u−gt0=vsin⁡θu=g+qEmt0=2gt0

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