Ncert Exercises & Solutions

4.22 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?

Length of the rod,

l = 0.45 m

Mass suspended by the wires,

m = 60 g = 60 \times 10^{- 3} kg

Acceleration due to gravity,

g = 9.8 m / s^{2}

Current in the rod flowing through the wire,

I = 5 A

(a) Magnetic field (B) is equal and opposite to the weight of the wire i.e.,

BIl = mg

∴ B = \frac{mg}{Il}

= \frac{60 \times 10^{- 3} \times 9.8}{5 \times 0.45} = 0.26 T

A horizontal magnetic field of 0.26 T normal to the length of the conductor should be set up in order to get zero tension in the wire. The magnetic field should be such that Fleming's left hand rule gives an upward magnetic force.

(b) If the direction of the current is reversed, then the force due to magnetic field and the weight of the wire acts in a vertically downward direction.

Total tension in the wire=BIl+mg

= 0.26 \times 5 \times 0.45 + (60 \times 10^{- 3}) \times 9.8

= 1.176 N

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