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Question: A horizontal wire of length \[10cm\]and mass \[0.3g\]carries a current of \[5A\]. The magnitude of t...

A horizontal wire of length 10cm10cmand mass 0.3g0.3gcarries a current of 5A5A. The magnitude of the magnetic field which can support the weight of the wire is (g=10m/s2)\left( {g = 10m/{s^2}} \right) .
A. 3×10−3T3 \times {10^{ - 3}}T
B. 6×10−3T6 \times {10^{ - 3}}T
C. 3×10−4T3 \times {10^{ - 4}}T
D. 6×10−4T6 \times {10^{ - 4}}T

Explanation

Solution

As we know that the force of a current carrying conductor will increase if the magnetic field strength increases, length of the conductor increases and Current passing from the conductor increases, As force is directly proportional to the magnetic field strength, current and the length of the conductor.

Formula used:
F=BIlF = BIl ,
Here F is the force on the conductor, B is the magnetic field, I is the current flowing in the conductor and l is the current flowing from the conductor. As the magnitude of the magnetic field supports the weight of the wire, we find the equilibrium state by taking, F=mgF = mg .

Complete step by step answer:
Current passes through horizontal wire- 5A5A
Length of the horizontal wire- 10cm=0.1m10cm = 0.1m
Mass of the wire is 0.3g=0.3×10−30.3g = 0.3 \times {10^{ - 3}}
g=10m/s2g = 10m/{s^2}
So, weight of the wire is mg=0.3×10−3×10=0.003N mg = 0.3 \times {10^{ - 3}} \times 10 = 0.003N
Assume B is the magnetic field strength applied to the horizontal wire.
As we know,
F=BIlF = BIl
Here F is force, B is the magnetic field, I is current and l is the length of the wire.
F=B×0.1×5F = B \times 0.1 \times 5
⇒F=0.5B\Rightarrow F = 0.5B
In equilibrium,
We know,
F=mgF = mg
Now, equate these two things, we get-
0.5B=0.0030.5B = 0.003
⇒B=0.0030.5\Rightarrow B = \dfrac{{0.003}}{{0.5}}
∴B=0.006T\therefore B = 0.006T
So, the magnetic field is 6×10−3T6 \times {10^{ - 3}}T.

Hence Option B is correct.

Note: Direction of magnetic field on a current carrying wire can be determined by right hand rule, which states that the direction of current represented by thumb and curling of finger represents the direction of magnetic field. If the thumb is in the upward direction, then the direction of the magnetic field will be anticlockwise and if the thumb is in downward direction then the magnetic field direction will be clockwise.