Question
A circular wire-loop of radius a carries a total charge Q distributed uniformly over its length. A small length dL of the wire is cut off. Find the electric field at the centre due to the remaining wire.
✓
Answer
$\frac{\text{Charge}}{\text{Unit length}}=\frac{\text{Q}}{2\pi\text{a}}=\lambda;$ Charge of $\text{d}\ell=\frac{\text{Qd}\ell}{2\pi\text{a}}\text{C}$
Initially the electric field was ‘0’ at the centre. Since the element ‘dℓ’ is removed so, net electric field must $\frac{\text{K}\times\text{q}}{\text{a}^2}$
Where q = charge of element $\text{d}\ell$
$\text{E}=\frac{\text{Kq}}{\text{a}^2}$
$=\frac{1}{4\pi\in_0}\times\frac{\text{Q}\text{d}\ell}{2\pi\text{a}}\times\frac{1}{\text{a}^2}$
$=\frac{\text{Qd}\ell}{8\pi^2\in_0\text{a}^3}$
Initially the electric field was ‘0’ at the centre. Since the element ‘dℓ’ is removed so, net electric field must $\frac{\text{K}\times\text{q}}{\text{a}^2}$
Where q = charge of element $\text{d}\ell$
$\text{E}=\frac{\text{Kq}}{\text{a}^2}$
$=\frac{1}{4\pi\in_0}\times\frac{\text{Q}\text{d}\ell}{2\pi\text{a}}\times\frac{1}{\text{a}^2}$
$=\frac{\text{Qd}\ell}{8\pi^2\in_0\text{a}^3}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A parallel beam of monochromatic light of wavelength 663nm is incident on a totally reflecting plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per second is $1.0 × 10^{19}$. Calculate the force exerted by the light beam on the mirror.
→If work function of the metal is $3.31 \times 1.6 \times$ $10^{-19}$ Joule, then calculate its threshold frequency in hertz.
→State the factor, which controls (i) wavelength of light and (ii) intensity of light, emitted by a LED.
Consider a circuit containing an ideal battery connected to a resistor. Do "work done by the battery" and "the thermal energy developed" represent two names of the same physical quantity?
Two long straight parallel wires A and B separated by a distance d, carry equal current I flowing in same direction as shown in the figure.
- Find the magnetic field at a point P situated between them at a distance x from one wire.
- Show graphically the variation of the magnetic field with distance x for 0 < x < d.
A conducting circular loop of radius a is connected to two Iong, straight wires. The straight wires carry current I as shown in figure. Find the magnetic field B at the centre of the loop.
- An em wave is travelling in a medium with a velocity $\overrightarrow{\text{v}} = \text{v}\hat{\text{i}}.$ Draw a sketch showing the propagation of the em wave, indicating the direction of the oscillating electric and magnetic fields.
- How are the magnitudes of the electric and magnetic fields related to the velocity of the em wave?
Compare the direction of the magnetic field inside a solenoid with that of the field there if the solenoid is replaced by its equivalent combination of north pole and south pole.
Consider a gold nucleus to be a sphere of radius 6.9 fermi in which protons and neutrons are distributed. Find the force of repulsion between two protons situated at largest separation. Why do these protons not fly apart under this repulsion?
What is called equipotential surface? Draw equipotential surfaces for point charges and write their properties.