Question

A current of 1.5 A is maintained in a copper wire of length 1 m with area of cross-section 1.7 × 10⁻⁷ m². The magnitude of electric field in the wire is ______.

[ρ_Cu = 1.7 × 10⁻⁸ Ω m]

Options

• `0.15 V/m`

• `0.30 V/m`

• `1.5 V/m`

• `3.0 V/m`

Answer 1

A current of 1.5 A is maintained in a copper wire of length 1 m with area of cross-section 1.7 × 10⁻⁷ m². The magnitude of electric field in the wire is `bbunderline(0.15 V/m)`.

Explanation:

Given: Current (I) = 1.5A

Length (l) = 1 m

Area of cross-section (A) = 1.7 × 10⁻⁷ m²

Resistivity (ρ) = 1.7 × 10⁻⁸ Ω m

Resistance (R) = `rho l/A`

= `(1.7 xx 10^-8 Omega*m) * (1 m)/(1.7 xx 10^-7 m^2)`

= 10⁻¹ Ω

Using Ohm’s Law:

V = IR

= 1.5 A × 0.1 Ω

= 0.15 V

The electric field in a uniform wire is the potential difference per unit length:

E = `V/I`

= `(0.15 V)/(1 m)`

= 0.15 V/m