An infinitely long thin wire, having a uniform charge density per unit length of 5 n C / m , is passing through a spherical shell of radius 1 m , as shown in the figure. A 10 n C charge is distributed

Question

An infinitely long thin wire, having a uniform charge density per unit length of $5 n C / m$ , is passing through a spherical shell of radius $1 m$ , as shown in the figure. A $10 n C$ charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points $P$ and $R$ , in Volt, is $____$ . [Given: In SI units $\frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9}, ln 2 = 0.7$ . Ignore the area pierced by the wire.]

TestHub · Accepted Answer

due to wire: d V = − E ⋅ d x ∫ v P ​ v R ​ ​ d V = − ∫ 0.5 2 ​ x 2 kλ ​ d x v R ​ − v P ​ = − 2 kλ ln 0.5 2 ​ = − 2 × 9 × 1 0 9 × 5 × 1 0 − 9 × 2 × 0.7 = − 126 V due to sphere: v R ​ − v P ​ = 2 k Q ​ − 1 k Q ​ = − 2 k Q ​ = 2 − 9 × 1 0 9 × 10 × 1 0 − 9 ​ = − 45 V v R ​ − v P ​ = − 126 − 45 = − 171 V v P ​ − v R ​ = 171 V

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