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pshichka [43]
2 years ago
10

A circular loop of wire 75 mm in radius carries a current of 113 A. Find the (a) magnetic field strength and (b) energy density

at the center of the loop.
Physics
1 answer:
Roman55 [17]2 years ago
7 0

The magnetic field strength is 9.47 ×10⁻⁴ T

The energy density at the center of the loop is 0.36 J/m³

<h3>Calculating Magnetic field strength & Energy density </h3>

From the question, we are to find the magnetic field strength

The magnetic field strength of a loop can be calculated by using the formula,

B = \frac{\mu_{0} I}{2R}

Where  B is the magnetic field strength

\mu_{0} is the permeability of free space (\mu_{0}=4\pi \times 10^{-7} \ N/A^{2})

I is the current

and R is the radius

From the give information,

R = 75 \ mm= 75 \times 10^{-3} \ m

and I = 113 \ A

Putting the parameters into the formula, we get

B = \frac{4\pi \times 10^{-7} \times 113}{2 \times 75 \times 10^{-3} }

B = 9.47 \times 10^{-4} \ T

Hence, the magnetic field strength is 9.47 ×10⁻⁴ T

Now, for the energy density

Energy density can be calculated by using the formula,

u_{B}  = \frac{B^{2} }{2\mu_{0} }

Where u_{B} is the energy density

Then,

u_{B}= \frac{(9.47\times 10^{-4} )^{2} }{2 \times 4\pi \times 10^{-7} }

u_{B} = 0.36 \ J/m^{3}

Hence, the energy density at the center of the loop is 0.36 J/m³

Learn more on Magnetic field stregth & Energy density here: brainly.com/question/13035557

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