The magnitude J of the current density in a certain lab wire with a circular cross section of radius R = 2 . 50 mm is given by J = 3 . 00 × 10 8 r 2 , with J in amperes per square meter and radial distance r in meters. What is the current through the outer section bounded by r = 0 . 900 R and r = R ?

Assuming J → is directed along the wire (with no radial flow) we integrate, starting with equation. i = ∫ J → d A = ∫ 9 R / 10 R k r 2 2 π r d r = 1 2 k π R 4 - 0 . 656 R 4 Where k = 3 . 0 × 10 8 . Therefore, if R = 0 . 0025 m i = 1 2 × 3 × 10 8 × 3 . 14 × 0 . 0025 4 × 0 . 344 i = 6 . 33 × 10 - 3 A We obtain, i = 6 . 33 × 10 - 3 A .

E M B I B E

Principles Of Physics International Student Version>Chapter 26 - Current and Resistance>Problems>Q 51

MEDIUM

JEE Main

IMPORTANT

Earn 100

A common flashlight bulb is rated at $0.20 A$ and $3.2 V$ (the values of the current and voltage under operating conditions). If the resistance of the tungsten bulb filament at room temperature $(20 ° C)$ is $1.1 Ω,$ what is the temperature of the filament when the bulb is on? Temperature coefficient of resistance of filament is $α = 4.5 \times 10^{- 3} K^{- 1}$ .

Important Questions on Current and Resistance

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 26 - Current and Resistance>Problems>Q 52

An isolated conducting sphere has a

20 cm

radius. One wire carries a current of

1.0000020 A

into it. Another wire carries a current of

1.0000000 A

out of it. How long would it take for the sphere to increase in potential by

1000 V ?

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 26 - Current and Resistance>Problems>Q 53

A beam contains $4.5 \times 10^{8}$ doubly charged negative ions per cubic centimeter, all of which are moving north with a speed of $300 m s^{- 1}$ . What are the (a) magnitude (b) direction of the current density $\vec{J} ?$ (c) If the particle distribution is uniform across a cross-sectional area of $2.5 μ m^{2},$ what is the current?