The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?

Solution

Given,

$Current on first conductor, I_{1} = 300 A Current on second conductor, I_{2} = 300 A Distance between the conductors, r = 1.5 c m = 1.5 \times 10^{- 2} m Length of the conductor, l = 70 cm$

Using Biot -Savart law,

$F = \frac{μ_{0} I_{1} I_{2} l}{2 πr}$

This implies,

Force per unit length =

$\frac{F}{l} = \frac{4 π \times 10^{- 7} \times 300 \times 300}{2 π \times 0.015}$

= $1.2 {Nm}^{- 1}$

The total force between the wires is $F = f l$

$= 1.2 \times 0.70 N = 0.84 N .$

The force is repulsive since the current will flow in opposite direction in the two wires.

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

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Moving Charges And Magnetism

The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?

Some More Questions From Moving Charges And Magnetism Chapter

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