What happens to the magnitude of the magnetic field inside along solenoid if the current is...

Question:

What happens to the magnitude of the magnetic field inside along solenoid if the current is doubled?

a. It becomes four times larger.

b. It becomes twice as large.

c. It is unchanged.

d. It becomes one-half as large.

e. It becomes one-fourth as large.

Magnetic Field:

When conducting wire mounts on an armature in the form of a coil and a specific current flow in the coil, then around the armature, there would be a generation of the magnetic field takes place. The value of the magnetic field varies with the parameters current and wire's turn. Out of these parameters, if any parameters change, then the magnetic field's value also changes.

Given Data

• The initial current is {eq}{I_1} {/eq}.
• The final current is {eq}{I_2} = 2{I_1} {/eq}.

The expression of the magnetic field inside along the solenoid at initial current value is given by,

{eq}{B_1} = {\mu _0}N{I_1} {/eq}.

Similarly, the expression of the magnetic field inside along the solenoid at final current value is given by,

{eq}\begin{align*} {B_2} &= {\mu _0}N{I_2}\\ &= {\mu _0}N \times 2{I_1}\\ &= 2{\mu _0}N{I_1}\\ &= 2{B_1} \end{align*} {/eq}.

Here, {eq}{B_1} {/eq} and {eq}{B_2} {/eq} are the magnetic field inside along the solenoid at initial and final current values respectively, {eq}{\mu _0} {/eq} is the vacuum permeability and {eq}N {/eq} is the number of turns.

From the above calculation, one can observe that, if the current in the solenoid is double then the magnetic field inside a long the solenoid would be doubled (it becomes twice as large).

Thus, the correct option is (b).

What is a Magnetic Field?

from

Chapter 7 / Lesson 2
26K

Magnetic fields fill the space around all magnets, but they're impossible to detect with our own senses. We'll use a common tool to map out a magnetic field and then discuss ferromagnetic materials to see how a magnetic field can be used to create new magnets.