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Magnetic Fields

Physics – Electric Currents and Magnetic Fields

For the figure below how, large must the current be to produce a magnetic field of $2.0 \cdot 10^{-4} \text{T}$ at a distance of 2 cm from a wire as shown? What is the direction of the field at this point?

Figure

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Known

$\begin{equation*} \text{B} = 2.0 \cdot 10^{-4} \text{T} \end{equation*}$

$\begin{equation*} \text{d} = 0.02 \text{m} (2 \text{cm}) \end{equation*}$

$\begin{equation*} \mu_0 = 4 \pi \cdot 10^{-7} \frac{\text{Tm}}{\text{A}} \end{equation*}$

Relevant Equation

$\begin{equation*} \text{B} = \frac{\mu_0 \cdot \text{I}}{2 \cdot \pi \cdot \text{d}} \end{equation*}$

Find

current and field direction

Solve the equation for “I”:

$\begin{equation*} \text{I} = \frac{\text{B} \cdot 2 \cdot \pi \cdot \text{d}}{\mu_0} \end{equation*}$

Plug in the numbers:

$\begin{equation*} \text{I} = \frac{\left( 2.0 \cdot 10^{-4} \text{T} \right) \left( \cdot 2 \cdot \pi \cdot 0.02 \text{m} \right)}{\left( 4 \pi \cdot 10^{-7} \frac{\text{Tm}}{\text{A}} \right)} = \boxed{\text{I} = 20 \text{A}} \end{equation*}$

Finding the direction of the field: The right-hand rule.

Point thumb of right hand in direction of the current. Keep palm flat and thumb extended at a right angle to other fingers.
Leave thumb extended and fold fingers into palm.
Observe that the magnetic field will follow your fingers (knuckle to fingertip).

$\begin{equation*} \boxed{ \begin{matrix} \text{B is out of the board} \\ \text{B is out of the page} \end{matrix} } \end{equation*}$

Resulting field if current is coming out of page (like you are looking at the end of wire that current is coming out of)

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