The magnetic field inside a long straight solenoid is
A. Inversely proportional to current
B. Uniform
C. Zero
D. Strong at ends and weak in middle
Answer: Option B
Solution (By JKSSB Mock Tests)
Ideal solenoid interior has uniform magnetic field B = μ₀ n I, parallel to axis. Outside field weak. Used in electromagnets, relays. Uniformity for scientific instruments.
What is the mathematical relationship between the escape velocity (Ve) and the orbital velocity (Vo) of a satellite revolving very close to the surface of the Earth?
Explanation:
The orbital velocity of a satellite very close to Earth is Vo = sqrt(gR). The escape velocity from Earth's surface is Ve = sqrt(2gR). Therefore, substituting Vo into the escape velocity equation yields Ve = sqrt(2) * Vo. A satellite requires a 41.4% increase in speed to escape orbit completely.
Explanation:
After n half-lives, activity reduces to (1/2)ⁿ of initial. Set (1/2)ⁿ = 1/16 ⇒ (1/2)ⁿ = (1/2)⁴ ⇒ n = 4 half-lives. Thus time = 4 × half-life. Memory aid: '1/2ⁿ remaining after n half-lives; 1/16 = 1/2⁴ ⇒ 4 half-lives'. This radioactivity calculation is frequently tested in competitive exams. Always express fraction as power of 1/2 to find half-life count. This problem assesses understanding of exponential decay without heavy computation.
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