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A circular loop of radius r carries a current i. at what distance along the axis of the loop is the magnetic field one-half its

lana [24]

At r = 0.766 R the magnetic field intensity will be half of its value at the center of the current carrying loop.

We have a circular loop of radius ' r ' carrying current ' i '.

We have to find at what distance along the axis of the loop is the magnetic field one-half its value at the center of the loop.

<h3>What is the formula to calculate the Magnetic field intensity due to a current carrying circular loop at a point on its axis?</h3>

The formula to calculate the magnetic field intensity due to a current carrying ( i ) circular loop of radius ' R ' at a distance ' x ' on its axis is given by -

$B(x) = \frac{\mu_{o} iR^{2} }{2(x^{2} +R^{2})^{\frac{3}{2} } }$

Now, for magnetic field intensity at the center of the loop can calculated by putting x = 0 in the above equation. On solving, we get -

$B(0) = \frac{\mu_{o} i}{2R}$

Let us assume that the distance at which the magnetic field intensity is one-half its value at the center of the loop be ' r '. Then -

$\frac{\mu_{o} iR^{2} }{2(r^{2} +R^{2})^{\frac{3}{2} } } = \frac{1}{2} \frac{\mu_{o}i }{2R}$

$2R^{3} = (r^{2} +R^{2} )^{\frac{3}{2} }$

$4R^{6} = (r^{2} +R^{2} )^{3}$

$r^{2} =0.587R^{2}$

r = 0.766R

Hence, at r = 0.766 R - the magnetic field intensity will be half of its value at the center of the current carrying loop.

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6 0

2 years ago

Which statement describes the law of conservation of energy?

dmitriy555 [2]

Answer:

D

Explanation:

cuz it transforms from one to another can't be created not destroyed.PERIOD!

6 0

3 years ago

Read 2 more answers

What is the Isotope notation for a Lithium atom?

Serggg [28]

Lithium has five isotopes, and each will have different notation. Lithium-7 is commonly used in salt and nuclear reactors. .ZAX , where X is the atomic symbol for the element, here Li for lithium, Z is the mass number, or the total number of protons and neutrons, and A is the atomic number, or the number of protons

6 0

3 years ago

11. A 6.0‐m wire with a mass of 50 g, is under tension. A transverse wave, for which the frequency is 810 Hz, the wavelength is

Irina-Kira [14]

Answer:

Time will be 19 ms so option (a) is correct option

Explanation:

We have given that mass of wire m = 50 gram = 0.5 kg

Frequency f = 810 Hz

Wavelength = 0.4 m

Velocity is given by

$v=wavelength\times frequency=810\times 0.4=324m/sec$

Amplitude is given as d = 6 m

So time $t=\frac{distance}{velocity}=\frac{6}{324}=0.01851=19ms$

So option (a) is correct option

4 0

4 years ago

When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude f = ax, where a is a constant. th

Veseljchak [2.6K]

Given:
F = ax
where
x = distance by which the rubber band is stretched
a = constant

The work done in stretching the rubber band from x = 0 to x = L is
$W=\int_{0}^{L} Fdx = \int_{0}^{L}ax \, dx = \frac{a}{2} [x^{2} ]_{0}^{L} = \frac{aL^{2}}{2}$

Answer: $\frac{aL^{2}}{2}$

4 0

4 years ago