Question

An electric motor is a device to convert electrical energy into mechanical energy. The motor shown below has a rectangular coil $(15cm\times 10cm)$ with $100$ turns placed in a uniform magnetic fleld $B=2.5T$. When a current is passed through the coil, lt completes $50$ revolutions in one second. the power output of the motor is $1.5kW$. The magnetic moment associated with the coil is

• A. $6.0\times {10}^{-2}A{m}^2$
• B. $4.5\times {10}^{-2}A{m}^2$
• C. 1.91 $\times {10}^{0}A{m}^2$
• D. 1.$5\times {10}^{-2}A{m}^2$

Answer 1

The correct option is C 1.91 $\times {10}^{0}A{m}^2$

Given : $\nu =50$ rps $P=1500$ W $B=2.5T$

Using $P=\tau w$ where $\tau =\mu B$ and $w=2\pi \nu$

$\therefore$ $P=\mu \left(2\pi \nu \right)B$

$⟹$ Magnetic moment, $\mu =\frac{P}{2\pi \nu B}=\frac{1500}{2\pi \left(50\right)\left(2.5\right)}=1.91$ $A{m}^2$