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An electron having mass 9.1×10⁻³¹ kg, charge 1.6×10⁻¹⁹ C and moving with the velocity of 10⁶ m s⁻¹ enters a region where magnetic field exists. If it describes a circle of radius 0.2 m then the intensity of magnetic field must be ______ ×10⁻⁵ T.

Asked in GUJCET 2018 · Circular motion: radius, period and energy

• (1) 14.4
• (2) 5.65
• (3) 2.84
• (4) 1.32

Step-by-step solution

Why the other options are wrong

• (1) The radius enters B=(mv)/(qr) once, not twice. Squaring it, qr²=1.6×10⁻¹⁹×0.04, gives 14.2×10⁻⁵ T — the only route to a number of this size, and not one the formula allows.
• (2) Reads 0.2 m as the diameter and uses r=0.1 m: (9.1×10⁻²⁵)/(1.6×10⁻¹⁹×0.1)=5.7×10⁻⁵ T. The stem gives the radius itself.
• (4) No single slip produces it: it is neither a factor of two nor a power of ten from the answer. Sanity check: (mv)/(qr)=(9.1×10⁻²⁵)/(3.2×10⁻²⁰)=2.84×10⁻⁵ T.

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