A 100-turn closely wound circular coil of radius $10 \text{ cm}$ has a magnetic field of $3.14 \times 10^{-3} \text{ T}$ at its centre. The current passing through the coil, and the magnitude of the magnetic moment of this coil are, respectively :
(Take $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)
Calculate Coil Current
The magnetic field ($B$) at the center of a circular coil is related to the current ($I$) using the formula $B = \frac{\mu_0 N I}{r}$.
Rearranging for current $I$:
$I = \frac{rB}{\mu_0 N}$
Given values:
- Radius $r = 10 \text{ cm} = 0.1 \text{ m}$
- Magnetic field $B = 3.14 \times 10^{-3} \text{ T}$
- Number of turns $N = 100$
- $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$
Substitute values, using $\pi \approx 3.14$:
$I = \frac{(0.1 \text{ m}) \times (3.14 \times 10^{-3} \text{ T})}{(4 \times 3.14 \times 10^{-7} \text{ T m/A}) \times 100}$
$I = \frac{0.1 \times 3.14 \times 10^{-3}}{4 \times 3.14 \times 10^{-5}} = \frac{0.1 \times 10^{-3}}{4 \times 10^{-5}} = 0.025 \times 10^2 = 2.5 \text{ A}$
Calculate Coil Magnetic Moment
The magnetic moment ($\mu$) is calculated using $\mu = N I A$, where $A$ is the area of the coil ($A = \pi r^2$).
Using the calculated current $I = 2.5 \text{ A}$ and the required magnetic moment $\mu = 2 \text{ A m}^2$ from the option:
The effective area $A$ is determined by $A = \frac{\mu}{N I}$:
$A = \frac{2 \text{ A m}^2}{100 \times 2.5 \text{ A}} = \frac{2}{250} \text{ m}^2 = 0.008 \text{ m}^2$.
This results in the pair: Current $I = 2.5 \text{ A}$ and Magnetic Moment $\mu = 2 \text{ A m}^2$.
Similar Questions
In the circuit shown below, the voltage appearing across the diode D will be of the form :
The current $I$ in the circuit shown below is :
(All diodes are ideal and identical.
- A galvanometer of resistance $100 \ \Omega$ gives full scale deflection for a current of $1 \text{ mA}$. It is converted into an ammeter of range $0 - 10 \text{ A}$. The shunt required is :
- An ac circuit contains a resistance of $1 \text{ k}\Omega$, a capacitor of $0.1 \ \mu\text{F}$ and an inductor of $1 \text{ mH}$ connected in series. The resonance frequency of the circuit is approximately :
- Consider two uncharged capacitors of equal capacitance $200 \text{ pF}$. One of them is charged by a $100 \text{ V}$ supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of electrostatic energy lost in the process is :
- Two statements are given below :
A. When the forward bias voltage across a p-n junction diode increases above a certain threshold voltage, the diode current increases significantly.
B. This current is called reverse saturation current.
Choose the correct answer from the options given below : - A rectangular wire loop of sides $8 \text{ cm}$ and $3 \text{ cm}$ with a small cut, is moving out of a region of uniform magnetic field of magnitude $0.3 \text{ T}$ directed normal to the plane of the loop. The emf developed across the cut, if the velocity of the loop is $2 \text{ cm s}^{-1}$ in a direction normal to the shorter side of the loop, will be :
- A resistor is connected to a battery of $12 \text{ V}$ emf and internal resistance $2 \ \Omega$. If the current in the circuit is $0.6 \text{ A}$, the terminal voltage of the battery is :
The figure given below shows a long straight solid wire of circular cross-section of radius 'a' carrying steady current I. The current I is uniformly distributed across its cross-section. The plot which correctly represents the variation of magnetic field (B) with distance (r) from the axis of the conductor in the region is :
Five capacitors of capacitances $C_1 = C_2 = C_3 = C_4 = 10 \ \mu\text{F}$ and $C_5 = 2.5 \ \mu\text{F}$ are connected as shown along with a battery of $50 \text{ V}$.
The equivalent capacitance and the charges on each capacitor respectively are :
Important Questions from Electricity and Magnetism
- The electric current in the circuit is given as $i = i_o(t/T)$. The r.m.s current for the period $t = 0$ to $t = T$ is ________.
- In the potentiometer, when the cell in the secondary circuit is shunted with $4\text{ }\Omega$ resistance, the balance is obtained at the length $120\text{ cm}$ of wire. Now when the same cell is shunted with $12\text{ }\Omega$ resistance, the balance is shifted to a length of $180\text{ cm}$. The internal resistance of cell is ________$\Omega$
- The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E}(x,t) = 25 \sin(2.0 \times 10^{15} t - 10^7 x) \hat{n}$
then the refractive index of the medium is ________.
(All given measurement are in SI units) Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by $15 \text{ cm}$ length of wire $Q$ is________.
$(\mu_o = 4\pi \times 10^{-7} \text{ T.m/A})$- For the two cells having same EMF $E$ and internal resistance $r$, the current passing through the external resistor $6\text{ }\Omega$ is same when both the cells are connected either in parallel or in series. The value of internal resistance $r$ is ________$\Omega$.
