A straight horizontal conducting rod of length `0*45m` and mass `60g` is suspended by two vertical wires at its end. A current of `5*0A` is set up in the rod through the wires. (a) What magnetic field should be set up normal to the conductor inorder that the tension in the wires is zero? (b) What will be the total tension in the wires if the direction of current is reversed, keeping the magnetic field same as before. (Ignore the mass of the wire) `g=9*8ms^-2`.

Explanation

(a) Arod of length I carrying a current I when placed in an uniform magnetic field B experiences a force of
`F = BIl`
Also, if m is the mass of the rod, then gravitational force acting on it is mg.

For the equilibrium of rod,
` 2 T + F = mg`
Given that , ` T = 0 `
` :. " " F = mg = BIl` ...(i)
`rArr " " B =(mg)/(Il) = (60 xx 9.8)/(1,000 xx 0.45 xx 5) `
` B = 0.26 T`
A horizontal magnetic field of magnitude `0.26` T normal to the conductor in such a direction that Fleming.s left-hand rule gives a magnetic force upwards.

For this situation, we have force acting on the rod due to external magnetic field in the downward direction.
From the figure,
`2T = F + mg`
From (i), `F = mg`
` :. " " 2T = mg + mg = 2mg`
` rArr" " T = mg = (60 xx 9.8)/1000 = 0.588 N`
Total tansion in the wires ` = 2 T = 2 xx 0.588 = 1.176 N`