2 marks) Use Gauss’ law to find the E-field outside of a long straight wire.
Question
2 marks) Use Gauss’ law to find the E-field outside of a long straight wire.
Solution
Sure, here is the step-by-step solution:
Step 1: Gauss's law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The Gaussian surface we choose is a cylindrical surface with the wire as the axis.
Step 2: The electric field E is radially outward and is constant on the cylindrical surface due to symmetry. Therefore, the electric flux through the curved surface of the cylinder is E * (2πrl), where r is the radius of the cylinder and l is the length.
Step 3: According to Gauss's law, this must be equal to the charge enclosed divided by the permittivity. The charge enclosed is λl, where λ is the linear charge density.
Step 4: Equating the two expressions gives E * (2πrl) = λl / ε₀. Simplifying this gives E = λ / (2πε₀r).
So, the electric field E outside a long straight wire of linear charge density λ is given by E = λ / (2πε₀r).
Similar Questions
A long straight wire of circular cross section of radius a carries asteady current I. The current is uniformly distributed across itscross section. The ratio of the magnitudes of magnetic field at apoint distant a/2 above the surface of wire to that at a point distanta/2 below its surface is(i) 4 :1(ii) 1:1(iii) 4: 3(iv) 3 :4
1. Ll___________________ 2. It is the electric field multiplied by the distance.___________________ 3. An emf induced by the motion of the conductor across the magnetic field.___________________ 4. It is the electric field E multiplied by the length.___________________ 5. States that the induced emf in a circuit is equal to the time rate of change of the magnetic flux through it.___________________ 6. A non-conservative field in the loop equal to the emf divided by the circumference of the loop.___________________ 7. Consists of coils of conductors that receive a voltage and produce magnetic flux.___________________ 8. They are electrical connections that are used to transfer power to and fro from the rotor of an AC generator.___________________ 9. It converts mechanical energy into electrical energy.___________________10. Force that makes the free charges in the rod moves, at the upper end creating an excess of positive charge and of a negative charge at the lower end.___________________11. Unit of a magnetic field.___________________12. A current measuring device.___________________13. Current caused by changing magnetic field in the circuit.___________________14. Equation of emf when v is not perpendicular to the field B.
A cylindrical wire of radius 0.5 mm and conductivity 5 × 107 S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x3π mA. The value of x is ____.
Electrical resistivity of a given metallic wire depends uponA its length. B its thickness. C nature of the material. D its shape.
Two long parallel wires are at a distance of 4 cm4 cm. They carry currents I𝐼 and 3I3𝐼 in same direction. Where will the field produced by both wires be zero from current I𝐼?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.