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3 years ago

6

Calculate the induced electric field in a 54-turn coil with a diameter of 19.5 cm that is placed in a spatially uniform magnetic

field of magnitude 0.5 T so that the face of the coil and the magnetic field are perpendicular. This magnetic field is reduced to zero in 0.1 seconds. Assume that the magnetic field is cylindrically symmetric with respect to the central axis of the coil.

1 answer:

storchak [24]3 years ago

4 0

Answer:

E = 3.049 N/C

Explanation:

Induced electric field = e/2 *(pi) *r

Induced electric field = e /(3.14 *19.5) - Eq (1)

e = (pi)r^2*B/t

= 3.14 * (19.5/2*100)^2 * 0.50 T/ 0.1

= 1.867 V

Substituting this value in equation 1, we get –

E = 1.867 V/(3.14 *19.5/100)

E = 3.049 N/C

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A thin spherical spherical shell of radius R which carried a uniform surface charge density σ. Write an expression for the volum

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Explanation:

From the given information:

We know that the thin spherical shell is on a uniform surface which implies that both the inside and outside the charge of the sphere are equal, Then

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$\rho (r) \ \alpha \ \delta (r -R)$

$\rho (r) = k \ \delta (r -R) \ \ at \ \ (r = R)$

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To find the constant k, we examine the total charge Q which is:

$Q = \int \rho (r) \ dV = \int \sigma \times dA$

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Thus;

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$\mathbf{\rho (r) = \delta* \delta (r -R) \ \ at \ \ (r=R)}$

$\mathbf{\rho (r) =0 \ \ at \ \ rR}$

To verify the units:

$\mathbf{\rho (r) =\sigma \ * \ \delta (r-R)}$

↓ ↓ ↓

c/m³ c/m³ × 1/m

Thus, the units are verified.

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$\mathbf{Q = 4 \pi R^2 \sigma }$

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