Current density in a cylindrical wire of radius R varies with radial distance as \beta( {r}+ {r}_{ {o}})^2. The current through the section of the wire shown in the figure. ( \beta is a constant)

Correct Answer is : πβ2[R44+r02R22+2r0R33]

\frac{\pi \beta}{2}[\frac{ {R}^4}{4}+r_0^2 \frac{ {R}^2}{2}+2 r_0 \frac{ {R}^3}{3}]

\frac{\pi \beta}{4}[\frac{R^4}{4}+r_0^2 \frac{R^2}{2}+2 r_0 \frac{R^3}{4}]

\frac{\pi \beta}{2}[\frac{ {R}^4}{2}+\frac{r_0^2 {R}^3}{2}+\frac{r_0 {R}^3}{3}]

\frac{\pi \beta}{2}[\frac{r_0^4}{4}+r_0^2 \frac{R^2}{2}+2 r_0 \frac{R^3}{3}]

AP EAPCET 12 July 2022 Shift 1 Paper

Question : 107 of 160

Marks: +1, -0

Current density in a cylindrical wire of radius R varies with radial distance as β(r+ro)2. The current through the section of the wire shown in the figure. ( β is a constant)

‌
πβ
2
[‌
R4
4
+r02‌
R2
2
+2r0‌
R3
3
]
‌
πβ
4
[‌
R4
4
+r02‌
R2
2
+2r0‌
R3
4
]
‌
πβ
2
[‌
R4
2
+‌
r02R3
2
+‌
r0R3
3
]
‌
πβ
2
[‌
r04
4
+r02‌
R2
2
+2r0‌
R3
3
]

Validate

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