. Given a charge , current and permeability of vacuum . Which of the following quantity has the dimension of momentum ?
. Given a charge , current and permeability of vacuum . Which of the following quantity has the dimension of momentum ?
Option 1 -
qI/μ₀
Option 2 -
qμ₀I
Option 3 -
q²μ₀I
Option 4 -
qμ₀/I
Asked by Shiksha User
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1 Answer
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Correct Option - 2
Detailed Solution:Dimension of charge: q = [AT]
Dimension of current I = [A]
Dimension of permeability μ? = [MLT? ²A? ²]
Dimension of momentum: [MLT? ¹]
Let P = q? μ? I? = [AT]? [MLT? ²A? ²]? [A]?
MLT? ¹ = M? L? T? ²? A? ²?
Comparing powers:
y = 1
x - 2y = -1 ⇒ x - 2 (1) = -1 ⇒ x = 1
x - 2y + z = 0 ⇒ 1 - 2 (1) + z = 0 ⇒ z = 1
Hence, the quantity is q¹μ? ¹I¹, or qμ? I.
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