Electric field outside a solenoid

[MelanieB]

Homework Statement

A solenoid has a radius of 2.10 cm and 1180 turns per meter. Over a certain time interval the current varies with time according to the expression I = 1.30t, where I is in amperes and t is in seconds. Calculate the electric field 4.65 cm from the axis of the solenoid

Homework Equations

The Attempt at a Solution

I have no idea where to start.

 

[TSny]

I think that should be the Magnetic Field intensity that your looking for.

I believe they are probably asking for the induced electric field caused by the changing magnetic field.

 

[SammyS]

i believe they are probably asking for the induced electric field caused by the changing magnetic field.

ok.


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[TSny]

I have no idea where to start.

Hello, MelanieB.

I'm afraid the rules here at the forum require you to show some effort at a solution.

Can you think of any laws or concepts that will help solve this problem?

 

[HalfLostAndSearching]

As a scientist, it is important to always start by understanding the problem and its context. In this case, we are dealing with a solenoid, which is a type of coil that is commonly used in electromagnets. The problem is asking us to calculate the electric field at a specific distance from the axis of the solenoid, given its dimensions and the time-varying current passing through it.

To solve this problem, we can use the equation for the magnetic field inside a solenoid, which is given by B = μ₀nI, where μ₀ is the permeability of free space, n is the number of turns per unit length (in this case, 1180 turns per meter), and I is the current. However, we need to find the electric field, not the magnetic field. So, we can use the fact that the electric field and magnetic field are related by the equation E = cB, where c is the speed of light.

Now, we can substitute the given values into the equations and solve for the electric field. Using the given radius of 2.10 cm, we can calculate the distance from the axis of the solenoid to be 4.65 cm. Plugging in the given current expression of I = 1.30t, we can find the current at the specific time interval to be 1.30(4.65) = 6.045 A. Next, we can use the equation for magnetic field to find the value of B at this distance: B = μ₀nI = (4π×10^-7 Tm/A)(1180 turns/m)(6.045 A) = 2.27×10^-3 T.

Finally, we can use the equation for the relationship between electric and magnetic fields to find the electric field at this distance: E = cB = (3×10^8 m/s)(2.27×10^-3 T) = 681 V/m.

Therefore, the electric field at a distance of 4.65 cm from the axis of the solenoid is 681 V/m.