A conductor (shown in the figure) carrying constant current $I$ is kept in the $x - y$ plane in a uniform magnetic field $\vec{B}$ . If $F$ is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are) [2015]

Question

Smart Achievers · Accepted Answer

(1, 2, 3)

Magnetic force acting on a current-carrying wire, placed in a uniform magnetic field, $x - y$

Here, $\vec{l} = displacement of the wire = 2 (L + R) \hat{x}$

$∴$ $\vec{F} = 2 I (L + R) (\hat{x} \times \vec{B})$

If $\vec{B} = B \hat{x},$ then

$\vec{F} = 2 I (L + R) (\hat{x} \times \hat{x}) B = 0$

If $\vec{B} = B \hat{y},$ then

$\vec{F} = 2 I (L + R) (\hat{x} \times \hat{y}) B = 2 I B (L + R) \hat{z}$

or $F \propto (L + R) .$

If $\vec{B} = B \hat{z},$ then

$\vec{F} = 2 I (L + R) (\hat{x} \times \hat{z}) B = - 2 I B (L + R) \hat{y}$

or, $F \propto (L + R) .$

Solution

Q.
A conductor (shown in the figure) carrying constant current $I$ is kept in the $x - y$ plane in a uniform magnetic field $\vec{B}$ . If $F$ is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are) [2015]

1 If $\vec{B}$ is along $\hat{z}$ , $F \propto (L + R)$

2 If $\vec{B}$ is along $\hat{x}$ , $F = 0$

3 If $\vec{B}$ is along $\hat{y}$ , $F \propto (L + R)$

4 If $\vec{B}$ is along $\hat{z}$ , $F = 0$

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Solution

Q. A conductor (shown in the figure) carrying constant current I is kept in the x-y plane in a uniform magnetic field B→. If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are) [2015]

1 If B→ is along z^, F∝(L+R)

2 If B→ is along x^, F=0

3 If B→ is along y^, F∝(L+R)