A 70.0-cm length of a cylindrical silver wire with a radius of 0.175 mm is extended horizontally between two leads. The potential at the left end of the wire is 3.15 V, and the potential at the right end is zero. The resistivity of silver is 1.586 ✕ 10−8 Ω · m.
a. What are the magnitude and direction of the electric field in the wire?
b. What is the resistance of the wire?
c. What are the magnitude and direction of the current in the wire?
d. What is the current density in the wire?

(a) the magnitude and direction of the electric field in the wire is 4.5 N/C towards the left end of the wire.

(b) the resistance of the wire is 0.1154 Ω

(c) the magnitude and direction of the current in the wire is 27.3 A towards the left end of the wire

(d) the current density in the wire is 4.053 x 10⁸ A/m³

Explanation:

Given;

Length of cylinder = 70cm = 0.7m

radius of cylinder = 1.75 x 10⁻⁴ m

potential V = 3.15 V

resistivity = 1.586 ✕ 10⁻⁸ Ω · m

Part (a) the magnitude and direction of the electric field in the wire

V = E x d

E = V/d

E = 3.15/0.7 = 4.5 N/C towards the left end of the wire.

Part (b) the resistance of the wire

R = 0.1154 Ω

Part (c) the magnitude and direction of the current in the wire

V = IR

I =V/R

I = 3.15/0.1154

I = 27.3 A towards the left end of the wire

Part (d) the current density in the wire

current density,J  = current /volume

volume = πr²h = π x (1.75 × 10⁻⁴)² x 0.7 = 6.7357 x 10⁻⁸ m³

J = 4.053 x 10⁸ A/m³

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.