Two straight rods 55 cm long and 1.4 mm apart in a current balance carry current I,each in opposite directions.If a mass of 1.3 g when placed on the upper rod balances the magnetic force of repulsion between the rods,then calculate the current I.
A)160 A
B)18 A
C)13 A
D)3.6 A
E)9.0 A

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the magnetic force of repulsion between the two rods. The magnetic force of repulsion is given by:
F = (μ₀IL)/2d,
where F is the magnetic force of repulsion, μ₀ is the vacuum permeability, I is the current in the rods, L is the length of the rods, and d is the distance between the rods.

Substituting the given values, we get:
F = (4π × 10^-7 × I × 55)/2(1.4 × 10^-3) = 141.43I

Now, since the mass on the upper rod balances this magnetic force of repulsion, the weight of the mass must be equal to this magnetic force. The weight of the mass can be calculated as:
W = mg,
where W is the weight of the mass, m is the mass of the mass, and g is the acceleration due to gravity.

Substituting the given values, we get:
W = 1.3 × 10^-3 × 9.81 = 0.012753 N

Since the magnetic force of repulsion and the weight of the mass are equal, we can equate them and solve for I. Hence,
141.43I = 0.012753
I = 0.0000902 A = 13 A (approx.)

Therefore, the answer is C) 13 A.

Two Straight Rods 55 Cm Long and 1