Question

If the current in a wire increases from 5A to 10A, what happens to its magnetic field?

Answer 1

If the current in a wire increases from 5A to 10A, the magnetic field generated will also be doubled.

Introduction

Hi ! I will help you to discuss about "magnetic field around a conducting wire". A conducting wire that carried electric current can generate amount of magnetic fields. In a standard winding condition, the increase number of electric current will be proportional to the increase number of the generated magnetic field. In other condition, the increase in distance (between center of field with a point) will be inversly proportional to the increase in the generated magnetic field. So, the magnetic field that generated around a current-carrying wire can be expressed in the following equation.

`\boxed{\sf{\bold{B = (\mu_0 \cdot I)/(2\pi \cdot d)}}}`

With the following condition:

• B = perceived magnetic field at a point (Wb/m² or T)
• 
  `\sf{\mu_0}` = vacuum permeability =
  `\sf{4\pi * 10^(-7) \: Wb/A.m}`
• I = electric current (A)
• d = distance of a point from the wire (m)

Problem Solving

We can assume that:

• Only the increase in current affects the change in the value of the magnetic field.
• Other provisions such as the distance of the point from the conducting wire is considered the same.

We know that :

• 
  `\sf{I_1 : I_2}` = 5 : 10 = 1 : 2 >> the ratio between the current flowing in first and second sample.
• 
  `\sf{d_1 : d_2}` = 1 : 1

What was asked ?

• B = perceived magnetic field at a point = ... : ...

Step by step :

`\sf{B_1 : B_2}`

`\sf{\frac{\cancel{\mu_0} \cdot I_1}{\cancel{2\pi} \cdot d_1} : \frac{\cancel{\mu_0} \cdot I_2}{\cancel{2\pi} \cdot d_2}}`

`\sf{(I_1)/(d_1) : (I_2)/(d_2)}`

`\sf{(I_1)/(\cancel d) : (I_2)/(\cancel d)}`

`\sf{I_1 : I_2}`

`\boxed{\sf{\bold{1 : 2}}}`

Conclusion

From the above comparison, we can see that the ratio of the magnetic field at a point will be the same as the ratio of the current flowing through the conducting wire is 1 : 2. So, The magnetic field generated will also be doubled.

Answer 2

If the current in a wire increases from 5 A to 10 A, the magnetic field will double.