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The ratio of magnetic fileds of a dipo...

The ratio of magnetic fileds of a dipole at a distance d in the broadside - on position to end - on position is .

A

Zero

B

infintiy

C

2

D

`(1)/(2)`

Text Solution

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The correct Answer is:
To find the ratio of the magnetic fields of a dipole at a distance \(d\) in the broadside-on position to the end-on position, we can follow these steps: ### Step 1: Understand the Positions - **End-on position (Axial position)**: This is when the point of observation is along the axis of the dipole, in line with the magnetic moment. - **Broadside-on position (Equatorial position)**: This is when the point of observation is perpendicular to the axis of the dipole. ### Step 2: Magnetic Field in the End-on Position The magnetic field \(B_1\) at a distance \(d\) from the dipole in the end-on position can be given by the formula: \[ B_1 = \frac{2\mu_0}{4\pi} \cdot \frac{m}{d^3} \] Here, \(m\) is the magnetic moment of the dipole, and \(\mu_0\) is the permeability of free space. ### Step 3: Magnetic Field in the Broadside-on Position The magnetic field \(B_2\) at a distance \(d\) from the dipole in the broadside-on position can be given by the formula: \[ B_2 = \frac{\mu_0}{4\pi} \cdot \frac{m}{d^3} \] ### Step 4: Calculate the Ratio Now, we can find the ratio of the magnetic fields in the broadside-on position to the end-on position: \[ \text{Ratio} = \frac{B_2}{B_1} = \frac{\frac{\mu_0}{4\pi} \cdot \frac{m}{d^3}}{\frac{2\mu_0}{4\pi} \cdot \frac{m}{d^3}} \] This simplifies to: \[ \text{Ratio} = \frac{1}{2} \] ### Step 5: Conclusion Thus, the ratio of the magnetic fields of a dipole at a distance \(d\) in the broadside-on position to the end-on position is: \[ \frac{1}{2} \]
To find the ratio of the magnetic fields of a dipole at a distance \(d\) in the broadside-on position to the end-on position, we can follow these steps: ### Step 1: Understand the Positions - **End-on position (Axial position)**: This is when the point of observation is along the axis of the dipole, in line with the magnetic moment. - **Broadside-on position (Equatorial position)**: This is when the point of observation is perpendicular to the axis of the dipole. ### Step 2: Magnetic Field in the End-on Position The magnetic field \(B_1\) at a distance \(d\) from the dipole in the end-on position can be given by the formula: ...
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