A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_{0} \hat{j}$ as shown in the figure. The magnetic force on the wire if it has a current i is [2024]

Question

Smart Achievers · Accepted Answer

(1)

Note: Direction of magnetic field is in $+ \hat{k}$

Force on current carrying wire,

$\vec{F} = i \vec{ℓ} \times \vec{B}$

Here, $ℓ = 2 R$

$\Rightarrow \vec{F} = - 2 i R B \hat{j}$

Solution

Q.
A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_{0} \hat{j}$ as shown in the figure. The magnetic force on the wire if it has a current i is [2024]

1 $- 2 i B R \hat{j}$

2 $2 i B R \hat{j}$

3 $- i B R \hat{j}$

4 $i B R \hat{j}$

Ans.
(1)

Note: Direction of magnetic field is in $+ \hat{k}$

Force on current carrying wire,

$\vec{F} = i \vec{ℓ} \times \vec{B}$

Here, $ℓ = 2 R$

$\Rightarrow \vec{F} = - 2 i R B \hat{j}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field B=B0j^ as shown in the figure. The magnetic force on the wire if it has a current i is [2024]

1 -2iBRj^

2 2iBRj^

3 -iBRj^

4 iBRj^

Ans. (1) Note: Direction of magnetic field is in +k^ Force on current carrying wire, F→=iℓ→×B→ Here, ℓ=2R ⇒F→=-2iRBj^