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A charge q₂ of mass m revolves around a stationary charge q₁ in a circular orbit of radius r. The orbital period of q₂ would be _____

Asked in GUJCET 2011 · Postulates, radius, speed and angular momentum

• (1) [(4π²mr³)/(kq₁q₂)]^1/2
• (2) [(kq₁q₂)/(4π²mr³)]^1/2
• (3) [(4π²mr⁴)/(kq₁q₂)]^1/2
• (4) [(4π²mr²)/(kq₁q₂)]^1/2

Step-by-step solution

Why the other options are wrong

• (2) This is the reciprocal of the period, 1/T — the number of revolutions per second. A period must get longer for a heavier charge or a bigger orbit, and this expression gets smaller with both.
• (3) r⁴ comes from writing the centripetal force as mv² without the 1/r: then mv²=(kq₁q₂)/(r²), v²=(kq₁q₂)/(mr²), and T=(2π r)/v picks up an extra power of r.
• (4) r² comes from using (kq₁q₂)/r, the potential-energy expression, as the force: then (mv²)/r=(kq₁q₂)/r, v²=(kq₁q₂)/m, and T=(2π r)/v loses a power of r.

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