A straight vertical conductor carries a current. At a point 5 cm due north of it, the magnetic induction is found to be $20\,\mu T$ due east. The magnetic induction at a point 10 cm east of it will be
- $5\mu T \,north$
- $10\mu T \,north$
- $5\mu T \,south$
- $10\mu T \,south$
The Correct Option is D
Solution and Explanation
Given:
Magnetic induction \(B_1 = 20 \, \mu T\) due east at a point 5 cm due north of the conductor.
- We need to find the magnetic induction \(B_2\) at a point 10 cm east of the conductor.
Identify the Given Magnetic Field:
\(B_1 = 20 \, \mu T\) due east at a point 5 cm due north of the conductor.
Direction of the Current:
The magnetic field \(B_1\) is eastward, which typically corresponds to a current flowing downward (along the negative z-axis) for a vertical conductor.
Magnetic Induction at 10 cm East:
At a point 10 cm east of the conductor, the magnetic induction \(B_2\) will have the same horizontal component as \(B_1\) because we are in the same horizontal plane of the conductor's magnetic field.
Therefore, the magnetic induction \(B_2\) at a point 10 cm east of the conductor will be \(10 \, \mu T\) due south.
So, the correct option is (D): \(10 \, \mu T\) south
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Concepts Used:
Moving Charges and Magnetism
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Magnetism:
- The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
- And Magnetism is a property that is displayed by Magnets and produced by moving charges, which results in objects being attracted or pushed away.
Magnetic Field:
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.